Board Thread:Support Requests - Getting Technical/@comment-30841933-20161225011118/@comment-26437440-20161225185751

Wikia will freely do name changes (unless you're asking for a new name every month lol). They usually just redirect the old URL to the new one, and files will sometimes still use the old URL too

As far as custom domains though, no. I believe there are some larger wikis that used to have non-wikia URLs (WOWWiki, Uncyclopedia, etc) but that doesn't seem to be the case any more.