What's this type of hairdo called?
Offhand, I'd say it's a variation of the bouffant with a bun on top. It transcends generations. Here's a fairly famous painting by John Sloan:
And, almost a hundred years later, here's Captain Janeway:
Solution 1:
It's a chignon.
: a way of arranging a woman's hair by twisting it into a round shape at the back of the head or neck M-W
"Les Chignons des Années 40 à Aujourd'hui" Marie-Claire
Solution 2:
It's a sock bun.
Because one way of making it is to use a cut sock.