Kanye's name change is official, a judge just signed off on the mogul's petition to officially change his legal name to "Ye" ... according to new legal docs obtained by TMZ. Ye won't have a middle or last name either, just straight to the point.

The judge's approval comes just under two months after we first reported on Kanye filing legal docs in Los Angeles asking a court to give him a new moniker.

He's gone by "Ye" as a nickname for years and years now ... but now the shortened version of the name that's on his birth certificate is what Uncle Sam, and apparently everyone else, will be calling him going forward.

Kim still has "West" in her own surname ... even using it on her recent "Saturday Night Live" hosting gig ... so it will be interesting to see if she keeps it around as their divorce proceeds. However, our sources had previously told us she'll hang onto the name just like the couple's kids.