Yes, but they have very different characteristics. You can't just plug a hydrogen car into the grid and charge it anywhere, so the overnight charges that EV owners are accustomed to go away. The hydrogen fuel cells tend to be large and heavy, so they don't save weight and also lose luggage capacity relative to an EV of similar size.

And without great advances in hydrogen production, they tend to cost more to operate than gasoline powered vehicles.

The one perk is faster fillups for road trips or lacking infrastructure. Most EV owners wouldn't switch just for that.

I believe the name is hydrogen fuel cell. It takes hydrogen as a fuel and generates electricity like a battery, instead of combusting it like a typical gas powered motor

The output of a hydrogen fuel cell is water, so it is a fairly sustainable loop if you can capture the water and generate hydrogen from it. But you need an efficient process to convert water into hydrogen

That fuel cell is more like an engine than a battery. You have to get O2 into it, get waste heat out (harder than the engine because the temperature is lower), keep it from drowning in the water it makes, etc.

It is hard to see the fuel cell EV competing with a battery EV.