Yes but the option to change gender is literally pointless if a name reflects the opposite gender. It renders Fantasia useless for those of us who want to swap genders, or simply do not like our names.
I'd be happy with it being a paid function. Charge me 15 bucks, I'd pay it to change my name when/if I swap gender.
Also I would assume that there would be an internal log noting the history of characters created/renamed on every account. A character changing names should not be an issue on SE's end.