I wanna talk about Buck and his name, so here is my rant.
Buck prefers to be called Buck. That's the main point. That's pretty much the end of the conversation. It's very clear from the narrative in season 4, and his constant correction of his parents, that he wants to be called Buck and not Evan. He doesn't like being called by his legal first name, he doesn't resonate with it anymore.
Why is this so important, for a lot of reasons. Preferred names are as simple as "I want to be called this, so please call me this." It's a basic sign of respect, and how you respect a person through the way they want to be called and identified. It's the same as Bobby being called that instead of Robert, Eddie being called that instead of Edmundo, Hen being called that instead of Henrietta, and so on.
So why are there still conversations around Buck and his want to be called that instead of Evan? I know why, but for the sake of amicability, I won't mention it. What I will mention, are the two people that are allowed to call Buck Evan, and why those make sense.
The first and most important one is Maddie. She, very early on in the show, for the most part, called Buck Evan pretty interchangeably. This is for a few reasons. One, she is getting used to the name change, and anyone who has gone through that change can tell you that they make mistakes along the way. Two, she still likes calling him Evan, because it's her little brother's name. When she called/calls him Evan, there isn't any malice behind it. She was the only person to love him through and through since the day he was born, therefore, she gets Evan rights. I know many people, whether they are cis and go by a nickname or trans, that let people they love call them by their assigned name simply because they love them, and know they are loved in return (this isn't always the case but just a point I wanted to make). There isn't malice, just love. That is why Maddie can call him Evan.
Now, Eddie. Eddie's use of Evan is one of the most talked about things especially when it comes to the buddie community. But I'm going to talk about why Eddie doesn't necessarily get Evan privileges the way Maddie does, and how I don't think he will use it often, or at all, in the future.
Eddie called Buck Evan for two reasons. One was to get his attention and to call Buck out of his mental spiral. Eddie knew that Buck was spiraling, and the unnaturalness of Eddie calling Buck by his first name would pull him into the moment. The second was for the narrative purpose of showing the audience that Eddie knew Buck more than anyone else, which was especially important for Buck's story for the season, and that episode alone. There were three moments that I can think of where Buck's reckless actions were misunderstood, strictly from season 4. When his mother was yelling at him in the flashback when he crashed his bike, when Taylor yelled at him for climbing up the construction rig where there was no protection, and when Bobby questioned said that it wasn't Buck's fault Eddie got shot. None of these things properly explained why Buck did those things. He knows he's not indestructible, invincible, or at fault for Eddie getting shot. That doesn't matter to him. All he can think about is how it wouldn't matter if he died or was the one who got shot because he believed to his core that he is expendable. That his presence in other people's lives isn't enough, and that he will always be the outlier that is able to be lost.
It isn't true, but it's what he believes. And only one person understands that. Eddie.
So when Eddie called Buck Evan, it was to negate everything that was swirling around in Buck's mind. It was a statement of "I know you, I see you, I understand you, and I love you."
Other than in that moment, Eddie never calls Buck Evan. Simply for what I already said. He knows Buck, sees him, understands him, and loves him.
To repeat what I said up at the top, Buck asking people to call him Buck is a simple preference and sign of respect. Other than Maddie and Eddie, everyone else in his life respects that. The people who don't call Buck Buck, don't fully respect or understand him. It's as simple as that.