Your display name is the large name shown on your public page. It is separate from your username, which is the melo.bio/yourname part of your address.
Where to change it
Dashboard, Profile, then the name field. It saves with the rest of your profile and updates on your public page straight away.
What is allowed
Most things, including spaces, emoji and non-Latin scripts. There is a length limit, and the same content rules apply as everywhere else: no impersonating someone else, no slurs, nothing that would break the Community Rules.
Display name against username
Changing your display name does not change your link, and there is no cooldown, so change it as often as you like. Changing your username does change your link and is rate limited. If you want to change what people see rather than where they land, the display name is the one you want.