I should have said that you can get much of what you want from the SYSTEM_USER built in function and by using DBCC INPUTBUFFER to populate a table with details of the call made to the server. But you can't get anything with EVENTDATA in a DML trigger.

edit: Also, you probably want to include both CURRENT_USER and SYSTEM_USER in case they are different. SYSTEM_USER is the original login that caused this call; CURRENT_USER is the current security context, which may be ueless if you want the original login but is very useful if you want the current context; often, but not always, they are the same but sometimes they are different.