what is this gymnastics move called?

You see it a lot in martial arts movies. For example, whenever the bad guy falls on the ground lying on his back, he will bring his knees up to chest level and then will rapidly extend his legs and then somehow he is standing again.

Is there a name for that move and how is it done?

I think you’re describing a “kip up”. Here’s a video (not of especially high quality).

Something I’m curious about: The term “kip up” doesn’t seem to be known to a lot of people. I distinctly remember junior high gym teachers calling it that and making us try to do the damned things. Do they do that anymore? Your average kid was about as good at doing that as climbing those stupid ropes, and simply wound up sitting on his ass on the mat. But it seemed like a skill the average person could learn if they really wanted to practice at it, not something insanely difficult.

They definitely tried to make us do kip-ups in high school in the early sixties.

I could never do a kip-up, to my eternal shame. I mean, I was on the varsity wrestling team, for crying out loud - how hard can a kip-ip be?

It’s not a move that’s ever used in gymnastics. There are other similar moves for low level gymnasts on other equipment called a kip up though. On the floor, it’s just clumsy and awkward.

Link to instructional video.

Here’s one done without help from the hands.

It can also be called a neck kip in traditional (artistic) gymnastics. A plain kip in gymnastics is one of the fundamental skills on uneven bars/high bar…not necessarily a “low level” skill, but one that must be mastered by gymnasts to progress to higher levels.

In addition to highbar and uneven bars, it is used on the parallel bars and rings. In general, when you see a higher level gymnast doing it, it’s because they fell off. It is a useful skill to get yourself into position to do more difficult maneuvers. I guess the beginning of routines often have them. A common highbar start is a kip-up free-hip, which puts you into a brief handstand on top of the bar.

Ditto that ‘kips’ in gymnastics usually refer to a move on bars or rings. However, in order to do that move on the floor, you just need strong abs. I can remember playing around at the gym one day during our warm-up period - all of us could do kip ups on the floor without trouble, but then again, we all had the hard-core abs that come with doing bars. (Why do you need all that abdominal strength? Because once you kick your legs, your core has a lot of work to do to make sure your upper body follows.)