Are there still problems with the name change for PSN?

At that time there were still problems with the name change for PSN, for example that the correct name ingame was not displayed or that there were problems using the online mode. Are there still such problems or has it been fixed?

Still exists in some games.

Is there a current list where you can view these games?

Wouldn't be known to me. It can also be a good thing that you have no problems. I know such and such, but I would probably not consider it myself, because sometimes trophies disappear, or are not unlocked at all.