I’ve used same format on emailing professors about my name multiple times. It’s clear and succinct, which makes it like the best or something.

Mr/Ms/Mrs/Dr/Prof [Last name],

I am a student in your [Name of course] class next semester. The roster will list me as my legal name, [Birth name]; however, I prefer to be addressed as [Chosen name] and with [female/male] pronouns [he/she], [him/her], [his/hers]. Please also forward this to the appropriate T.A. or assistant or let me know who they are so that I may inform them of this preference as well.

Thank you very much.

Sincerely,

[Chosen name]

Credit goes to some university (was it U of Colorado? I think it was)