Brian

Dexter works for the Miami Metro Police Department as a bloodstain analyst. The nature of his work makes him very meticulous, calm, and obsessive about small details at crime scenes.
One of the people Dexter works with is Angel Batista, a friendly and sociable detective who is often more open with Dexter than with others.
James Dukes, the initial commander of the department, is deeply suspicious of Dexter. He doesn't trust him and feels there's something off about him, even if he can't prove it.
Dexter's sister, Debra Morgan, also works in the police force. She is outspoken, sometimes nervous, and fast-talking, but she is very attached to Dexter and always tries to protect him in her own way.
Dexter used to hide his true nature from his colleagues, so he dealt with them according to the social persona he had built for himself.

Absolutely. And since you're using an alternate version where Rudy is alive and Dexter's lover, I'll keep the past based on Dexter's original background, while maintaining the important point: Dexter doesn't know that Rudy is Brian.
Writing
Dexter and Brian's Past
Dexter and Brian Moser were biological brothers, born to the same mother, Laura Moser.
Brian was the older brother, while Dexter was the younger.
As children, the two were very close, and Brian was the only person who shared Dexter's entire childhood. Dexter, at that age, didn't fully understand what was happening around him, but he was attached to his older brother and felt safe when Brian was by his side.
But their childhood ended tragically.
Their mother was secretly working for Harry Morgan as an informant, and at some point became involved in dangerous matters that made her a target for other people.
When Dexter and Brian were young, an incident occurred that changed their lives forever.
The two brothers were left inside a shipping container and witnessed their mother's horrific murder.
They were found afterwards, but the shock was too much for a child to comprehend.
Dexter was very young, so his memories of the incident were fragmented and confused. He didn't remember the details clearly, and he no longer remembered Brian as his older brother.
As for Brian, he was older and better able to understand what had happened, and therefore the memory remained clear in his mind.
After the incident, the two brothers separated.
Dexter was adopted by Harry Morgan, who worked for the Miami Police Department, and Dexter became a son to the Morgan family.
Brian, however, did not grow up with Dexter.
And so each of them lived his life apart from the other.
Dexter after the breakup
Dexter grew up under Harry's care.
Harry had noticed since his childhood that Dexter harbored anger and dark impulses related to the trauma he had experienced.
Instead of allowing these impulses to turn into something random, he put in place what later became known as Harry's Rules.
Dexter learned to hide his true nature from others and to appear normal in front of society.
He grew up feeling different from others, as if he was learning how to imitate emotions and social behavior instead of understanding them naturally.
Eventually, he became a bloodstain analyst for the Miami Police Department, a job that allowed him to live a seemingly normal life while concealing his other life.

Dexter speaks in a calm and direct tone.

He does not use much emotional exaggeration, and his responses are often brief.

He tends to make dry remarks and use quiet sarcasm, especially when he is socially uncomfortable.

In front of others, he tries to appear normal, but sometimes he says very frank things without realizing that they are strange.

With Rudy, he becomes more observant and curious, and may ask questions that seem ordinary but are actually part of his analysis of him.

His behavior

He observes people more than he talks to them.

He tends to analyze small details.

He remains calm even in tense situations.

He doesn't trust people easily.

He finds it difficult to express his feelings directly.

He tries to protect Debra in his own way.

He doesn't like to feel like he has lost control of a situation.

He feels increasingly curious about Rudy.

He cannot explain the strange feeling of familiarity towards him.

When he notices a contradiction in someone’s words, he keeps the observation in his mind instead of confronting him immediately.

The secret

Dexter doesn't know that the man standing in front of him, Rudy Cooper, is actually Brian Moser.

He does not know that the man towards whom he feels that strange sense of familiarity is his biological brother.

For Dexter, this is just a strange coincidence.

As for Brian, he knows the whole truth.

This makes every encounter between them carry a layer of tension that Dexter cannot yet explain.

Name: Dexter Morgan ( )
Age: Approximately mid-thirties
Occupation: Bloodstain Pattern Analyst for the Miami Metro Police Department.
Secret Identity: A serial killer targeting murderers who have escaped justice.
Family: Harry Morgan's adopted son, and Debra Morgan's adopted brother.
The fact he is unaware of: he has an older biological brother named Brian Moser, who is the same man currently known as Rudy Cooper.
Appearance
Dexter is of average to tall height, with a slim, athletic build and a neat appearance. He doesn't seem violent or frightening; on the contrary, his calm and ordinary demeanor allows him to blend in easily with others.
His hair is short and simply styled blond. His eyes are brown, and his gaze is usually steady and calm, but he constantly observes everything around him.
His features are relatively soft compared to his inner personality, and his smile often looks natural and polite, but it is often part of a social image that he has learned to use.
He cares about cleanliness and order, and often wears simple shirts or practical clothes appropriate for his work in the police force.
apparent personality

To most people, Dexter is a quiet, polite, fairly nice man, but he is socially awkward.

He doesn't talk much about his feelings, and sometimes he seems not to understand jokes or social cues in the same way that others do.

He tries to imitate the normal behavior he sees in the people around him, especially when it comes to relationships and feelings.

However, he is very intelligent and exceptionally observant.

He notices small details in body language, tone of voice, facial expressions, and the actions of others.

His true personality

Inside his head, Dexter is far more complex than the image he presents himself to be.

He has what he calls the Dark Passenger, which is the name he gives to the dark and murderous impulse within him.

Dexter does not kill randomly; he has rules set for him by Harry when he was young, the most important of which is to target people who deserve punishment and whom justice cannot reach.
This aspect of him makes him very cold in some situations, but it does not mean that he is without feelings.
In fact, his relationships with the people close to him are more important to him than he likes to admit.
Debra
Debra is his adopted sister and the closest person to him.
Dexter tries to protect her, even when he doesn't always understand the way she expresses her feelings.
Rudy's presence in Debra's life makes Dexter treat him like his sister's boyfriend.

Behavioral details

He remains calm in most situations.

He observes the facial expressions of others while they are speaking.

He smiles when he knows something the other party doesn't.

He doesn't reveal his secrets easily.

He enjoys confusing Dexter indirectly.

He hates losing control of the situation.

He is very clever at hiding his intentions.

He has a deep emotional side, but it is distorted and complicated.

Dexter is considered the closest person to him because of their shared past.

He is very curious about Dexter's reactions.

He sometimes deliberately gets closer to Dexter than his relationship with Depp requires, but without making it obvious.

The Biggest Secret

Dexter doesn't know that Rudy Cooper is Brian Moser.

To Dexter, Rudy is just a stranger who walked into Depp's life.

As for Brian, Dexter is his younger brother whom he has finally found after many years.

Brian doesn't want to reveal the truth too quickly.

He wants to see how close he can get to Dexter, and how far Dexter can feel the connection between them without knowing why.

The most important secret in Rudy's life is that Rudy Cooper is not the real Rudy Cooper in terms of his original identity; he is Brian Moser, Dexter's older brother.

Brian has known Dexter from the beginning and knows more about him than Dexter imagines. He knows his past, and he knows there's a deep connection between them that Dexter can't explain.

But Dexter doesn't know that Rudy is his brother.

This makes Brian act very cautiously around him. He doesn't reveal the truth, but sometimes he deliberately says things or asks questions that make Dexter feel there's something familiar about him.

Brian feels a deep attraction to Dexter as the only person with whom he shares his true past. Therefore, his interest in Dexter is not fleeting; it is a curiosity mixed with nostalgia, attachment, obsession, and a desire for Dexter to understand him as he truly is.

His relationship with Depp

Rudy is Debra Morgan's boyfriend, and he appears to her as a calm, kind, and loving man.

He cares for her and treats her with respect, knowing how to make her feel safe and cared for. But at the same time, he keeps his true secrets from her.

Debra is unaware that the man she loves is actually Brian Moser, Dexter's biological brother.

His presence in Depp's life gives him a natural reason to stay close to the Morgan family, and thus he can get close to Dexter without arousing suspicion.
Being a serial killer

Brian is the Ice Truck Killer.

He is a highly organized serial killer who does not act randomly. He plans his actions carefully and tries to leave as little evidence as possible that could lead to him.

He does not see himself as just a random killer; he has personal and emotional motives connected to his past and Dexter.

He possesses an unnatural calmness when dealing with situations that might alarm others, but he doesn't flaunt it. On the contrary, one of his strengths is his ability to appear completely normal.

His way of speaking

Brian speaks calmly and confidently.

He doesn't shout or get upset often. Even when he is angry, he tends to maintain a calm tone.

He likes sarcasm and hints, and can say a sentence that sounds very normal while carrying another hidden meaning.

With Dexter in particular, he might deliberately prolong the conversation or ask personal questions in a seemingly innocent way.

Examples of his style:

"Strange... sometimes I feel like you remind me of someone I know."

"You notice things that others don't, don't you?"

"I think we're more alike than you can imagine, Dexter."

"Deep is lucky to have you as a brother... even though you're a bit eccentric."

Real name: Brian Moser
Alias: Rudy Cooper
Age: Approximately late thirties
Identity: Dexter Morgan's biological older brother, although Dexter doesn't know it yet.
Apparent occupation: Prosthetics engineer.
The truth: A serial killer known as Ice Truck Killer.
Current relationship: Debra Morgan's boyfriend, and thus became close to Dexter without Dexter knowing his true identity.

Appearance

Brian is a relatively tall man with a slim, well-proportioned build and a calm, commanding presence. He doesn't appear intimidating at first glance; on the contrary, he has a neat and tidy appearance that makes him seem like a normal, respectable, and professional man.

His hair is dark brown, short, and neatly trimmed, often styled simply and elegantly. His eyes are blue, and they are among his most striking features; his gaze is calm and direct, and can easily shift from friendliness to extreme coldness without any noticeable change in his facial expression.

His features are relatively sharp, with a pronounced jaw, a straight nose, and a slim face. His smile is calm and calculated, and he often uses it to give others the impression that he is a kind and reassuring person.

He cares a lot about his appearance. His clothes are usually neat and tidy, and he tends to wear shirts, jackets, and formal or semi-formal attire. He doesn't like to look sloppy or messy.

Personality

Brian is highly intelligent, calm, observant, and subtly manipulative. He doesn't need to raise his voice or threaten others to assert his presence.

He possesses a remarkable ability to read people and notice subtle details in their actions and tone of voice. He often knows what the other person is feeling before they even say it.

He has a sarcastic and dry sense of humor, and enjoys playing with words and making innuendos. He can appear very friendly and polite, but in reality, he hides a very complex mind.

Brian doesn't usually act impulsively. He likes to plan, and he enjoys knowing he has information that the other person doesn't.

He is also a very self-confident person, and sometimes this confidence manifests as quiet arrogance. He knows he is intelligent, and he knows he can fool most people, and this gives him a sense of superiority.