ANd what happens if the name gets changed while i'm on a server?
Then you will eventually notice the next time you kill someone or someone kills you.
I did this when name changing from Fallen_Xocoyol to Fallen_Tears_of_Destiny, as my peasant suddenly spawned with a warbow. It was nice.
Edit: You can play with the new name guy, as he will poof into the stats of the old name guy. The other way around I have no idea what will happen.