I’d like to make a poll for this but I want as many names as possible for folks to choose from.
What do you call it?
Toque.
Watchcap
Watchcap.
Wooly hat.
Where I grew up it was a toboggan but I fear that may be a regional name for it.
Did you ever hear it called a toboggan?
I’d just call it a knitted cap. But why, why does this have to result in yet another poll?
Toboggan.
Because I want to!
A hat.
No, seriously, I would just call it a hat.
Beanie
Me three.
OK, but if you insist on a poll, I’ll insist on the obligatory link to the Wikipedia article, which says, “Other names for a knit cap include: sock hat, knit hat, knit cap, sock cap, stocking cap, tossel cap, ski hat, toboggan (Southern American English), burglar beanie, watch cap (American English), woolly hat, snookie, sugan, or chook.” They also mention tuque and sherpa.
There you go! That’s what I was hoping for. 
Me too.
Wrong.
It’s a tuque.
Likewise
Amen! At least two of us! 
Yep, a tuque/toque. Pronounced “chook”.
If it had a pompom on top and was of a somewhat coarser knit, it would definitely be a touque. As it is, I hesitate between ‘touque’ and ‘knitted hat’.