It depends on how you play your character. Some people change character names, genders and races twice a week wiothout much thought. I only used one fantasia so far. The reason why I am named Balipu Nakamu as a female Mi'qote is that I was originally a male Lalafell and according to my ingame story I just drank some booze at a party that changed me on the outside, but I am still the same person. I don't let my name bother me. Of course after I fantasia into an Au Ra Xaela I will change my name into something I didn't decide yet as according to my story I am secretly a sleeper agent sent to Aldernard with false memories and under a glamour untill I am strong enough to realise my destiny as the chosen one and united the warring tribes of the Xaela in a glorious war that will be remember throughout the ages. My memories will come back at the beginning of 3.0

TL,DR version. If you don't want to change your name you don't have to. You can be any race inside regardless of what you look in the outside.