So, I'm writing a story with a character who is a trans woman. Granted, It's not peak literature and I only have a small crowd following the story, but I like writing it. Anyway, at the start of the story this character has not yet come out to themselves and still goes by their old name. This changes as the story progresses since the character later comes out to themselves and then others. Is it OK to use their old name in narration before the character comes out? Such as describing what the character is doing and when she speaks. Likewise with pronouns. Then altering the narration in later chapters to reflect the coming out. Just to clarify, the coming out isn't the main plotline, or at least I don't want it to come across that way. I'd say that the main plot revolves around the friendship she has with another character (which later develops into a romance). However, I'd still like to hear people's opinions on the matter.
I've had this question myself before, and came to the conclusion that's completely fine. The character is discovering themself and that change of pronouns is part of that process, so conveying it by switching the pronouns and name is fine.