In casual English, you can use "they" and "their" to talk about a person without mentioning whether the person is male or female:
A: I have a friend who studies dance at the same studio.
B: Oh, what's their name?
In formal English, it's necessary to say "he" or "she" and "his" or "her":
If you'd like to contact one of the artists, please write your email address next to his or her name.