Not all are exactly synonyms, but they are used interchangeably in some instances (sometimes by people who may not know the correct terminology).

Name

Screen name

Nickname

Nick

User name

ID

User ID (or UID)

Alias

Screen alias

Login

Logon

Pseudonym

Account name

Account

Any of these not belong on the list? (not because they're incorrect, but because they're not really used like that)

I'm sure there must be a few other terms. Maybe this is a yart.