Does Magnus Carlsen have any openings/opening variations named for him? Does Magnus Carlsen have any openings/opening variations named for him?

The last world champion I know of to have an opening variation named for him was Anatoly Karpov (e.g. Caro-Kann, Karpov Variation or Karpov Variation in the Ruy Lopez).
In the old days variations were named after players who did serious theoretical work and/or played one line consistently over a longer period. 

As openings got more and more analyzed it got increasingly more difficult to find new variations comparable to those old masters. Nowadays the top players might find a novelty around move 20 or so. If you want, you could call those lines variation and credit them to the player. I am sure some websites do just that, but personally I see a big difference between say the Najdorf variation and those side lines.

So yes, probably somebody somewhere called something a Carlsen variation, but whether you consider it a variation is up to you. Also, perhaps it needs some more time until a line is called variation and maybe in 10 years people will agree to call a line Carlsen variation.