When your mom introduces her 'son' as her daughter, it is going to be a problem.
When your sister remarks her younger sister (you) and then adds some comment, it will be a problem.
When one of your children points you out in conversation as 'mom' it will be a problem.
When you are referred to as uncle not aunt, it will be a problem.
The name used is not always an issue based on the name. I am not Leslie I am Lesley. Not that it matters much when they always use Les. But if you are going from a blatantly female name to and utterly male name, it will grate on the nerves potentially. Going from Jane to Frank will be significant, and I can't picture a person liking being called Jane and looking like a Frank.
The thing is, as was pointed out, we were once all infants, and that means you were thought of exactly as you looked like naked.
My mom changed a little boys body and put a little boy into little boys clothing.
Telling everyone I am a woman, it loses something if I can't get changed with them in the correct change room and not stand there anatomically correct to my view of myself. Taking off a dress and then lingerie, and putting on a swim suit and not having some things just there to see tends to intrude on the desired image.
My mom is in the hospital, and if she needs to see a nurse and it involves a degree of undress, mom is going to feel awkward undressing in front of her 'son'. That is unlikely to change, and it tends to really slam home the truth of why so many of us refuse to avoid the operation.
I am not defined by my genitals, but, they most certainly limit my freedom all the same.
My mom accepts me fully, but, the ability to see me as her son likely will never turn off in favour of my being seen as a daughter until I can strip naked, expose minor breast development, and expose a vagina to view before putting them into a female swim suit or underwear.
Until I can walk around in a nighty and expose female genitals if I am not careful, I don't expect anyone to really see me as a woman.
Calling me Lesley Roberta what do much, if I know they are still seeing Leslie Robert.