Changing PSN log-in on one user
Solution 1:
There is no way to fix this PSN flaw.
On first online sign-in with a local user, that PSN name is permanantly associated with that local user. That PSN name is saved as read only; any attempt to log-in with another user name fails (as you have seen).
The only solution you have is to make a new local user and associate the correct PSN name with it.
Theortically, to backup all your save games and stuff you would attach some form of USB hard drive, copy over all user information, delete that account, create a new account with EXACT same name, and then copy over the data into the new user account.
WARNING: I have tried this twice for my girlfriend and once for another friend, none of those times was the save data or trophies able to be used by the new account.
DO AT YOUR OWN RISK