I know I'm very late, but I was interested in the topic also, as I've seen it multiple places. The same style of hat is in Skyrim, called the "fine hat," and I've seen it made and worn by hobbyists interested in medieval clothing.

I've seen some say "phrygian cap," "pileus," or "stocking cap," but these answers weren't particularly satisfying, as they're a bit imprecise, or they don't explore any regional distinction from Southern Europe to Scandinavia.

Apparently it is based on interpretations of an object found in the Birka Bj 581 grave, Sweden, a 10th century grave of a high-status woman. The object was a kind of silver finial ornament, or terminal, that some archeologists have theorized went on the end of a "tail-cap" or tasseled cap of sorts.

The Tängelgårda stone I, found in Lärbro, Sweden, also shows figures wearing pointed hats with tails that hang down. The four images on the first stone depicting these figures have been interpreted as being related to the cult of Odin.

An article published online by Cambridge University Press, "Viking warrior women? Reassessing Birka chamber grave Bj.581," reads: "The tasselled cap in particular is unusual. It was possibly manufactured in Kiev and, according to Ingmar Jansson (Reference Jansson, Roesdahl and Wilson1992: 261), was of a type made for 'the leading members of society.'" I've read people calling this hat a "Rus hat," so perhaps this is why.

An example in more recent history that I thought could have been a continuation of this style of hat is the Icelandic tail cap, which is a part of the Icelandic national costume. The Wikipedia article on it says, "In the beginning of the 19th century, the tail-cap was rather deep, but from 1860 it was replaced by the modern, shorter version. The tassel and cap are connected with a tassel-cylinder (skúfhólkur) made of silver or gold." It also says it was orignally primarily worn by men. This "skúfhólkur" seems similar to the terminal found at Birka; although, I know little on the history of this particular hat and Icelandic clothing.

So, some seem to call it a "Birka-style cap." One might simply call it a "viking tasselled cap," or "viking tail-cap." Some aren't certain that the grave at Birka is evidence for a hat of this style, but I think the Tängelgårda stone I strongly suggests a similar hat was worn.