I want to save the session UserName in a table using mysql.
I have the history of my base table(auction) update, delete, create information will get stored in a backup table(auction_log). I want to save username(who currently loged in and modifies the record in a table) too in the auction_log table.

well, you're the one who wrote the app that allowed the user to log in

so just use that name and save it along with the other data in the log table