I did not even know there was a name for it. I just call it my floor mop, and a very good one it is. I have no mechanical squeezer for removing surplus water. It is all done my physical strength, a rinse under running water and a tight squeeze by hand, but it works. You can see I have enough extra mop heads, as I use a fresh one daily. I have mainly stone tiled floors and my squeegee is excellent for keeping them clean with a daily wipe over, but just plain water. I do not need cleaning liquid, it would only make marks on the floor.
The job is quickly done and I can clean the mop heads in my washing machine. There is no doubt about it, I just love my Squeegee.