An admin like Gamerman1990 will need to set a block on the account. Because he's using computers that are assigned addresses at random and he's using different computers on different ISPs, that's why he can come back under a new account. But, I do have info on a few of those IP addresses so I can supply a few rangeblocks to slow him down.
He has not yet expressed an interest in The Wiggles, but I don't have any problems with you setting preemptive blocks there. He's the kind of person that is not going to give up any time soon, so it may be a while before he grows out of this, if he ever does.
You might not know this, but Caidin Johnson has kept returning recently with new sockpuppets. As a reminder, if we see any user with the name "Caidin", we'd better block him immediately before he wrecks the wiki.
I have been keeping track of him since he's shown he's not going to give up for quite a while and have placed blocks on his accounts over on a couple of wikis he's likely to hit. Most of his accounts do have his name or initials in them, but not all, and a lot of them fit a few patterns I've identified.
Which accounts are you referring to? Last confirmed one I have on Wikia is from a week ago, but he's used three on Wikipedia during this past week.