Go to your profile settings from the menu.

You can set:

• Display name — what people see on guest lists and RSVPs. Required.
• Profile photo — tap your avatar to upload a new one. It shows next to your name everywhere: guest lists, host info, your public profile.
• Bio — a few words about yourself. Optional.
• Instagram — tap "Add Instagram" to link your handle. It shows on your public profile.

Tap Save when you're done. Changes apply everywhere immediately.

See also: Your Public Profile, How RSVPs Work