Then tick the radio button Append primary and connection specific DNS suffixes and tick the box Append parent suffixes of the primary DNS suffix
That's good, just keep your eye on it for a while to make sure it doesn't come back.
Rebooted after changing name, no further "Duplicate name... " message after changing name!
I am sorry if I stepped on your toes, but this forum isn't only for USA people and the advice given might have caused some people to shoot into stress after they figure out they loose their internet connection. Just have to be careful and make sure that what you're doing is not going to scare/confuse the person you're trying to help.
I'm tired of getting lip from this guy, every time, I ask you to do something.
I have given him enough information to fix you're problem.
I'll let the "Trusted Tech Staff" take it from here.