changing display name on icloud email

i am using an iphone. i changed the name on my apple id a couple years ago when i came out, but all emails sent from my icloud email address have my old name as the display name. i can’t find an option to change it in settings or in the mail app itself. i’m sick of the confusion when i email someone and my display name doesnt match the name i actually go by 😔 is there a way to fix this or do i just have to suck it up and explain in every email that it’s not my name?