Login triggers fire early in the connection process, before the switch to the requested DB happens. That's why you need the 3-part table name and why you only see master.
As for the login name... ORIGINAL_LOGIN() is the function you want there.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability