When you start out you choose either the sister or the brother. Both have canon names (which I did not know starting out). Lumine is the sister, Aether the brother.
You then name them. And that is more or less the name of your account. The characters will never say your name so it is rather okay to still be immersed in the story.
You can change your nickname in the game itself but it does not have much of an impact. And I guess you can only change it in something that has not been chosen, yet? At least for connecting with others you need their number and not their name.
Have fun! 😀 (Back to Zhongli and my daily grind in the domains)