An undersea volcanic formation that does not rise at least 1000 meters above the surrounding sea floor is called a seamount.

Here's why:

* Seamount: A seamount is an isolated underwater mountain rising at least 1000 meters from the ocean floor, but not reaching the surface.

* Guyot: A guyot is a flat-topped seamount, usually formed by erosion.

* Volcanic ridge: A volcanic ridge is a long, elevated area of the seafloor formed by a chain of volcanoes.

* Mid-ocean ridge: A mid-ocean ridge is a massive underwater mountain range formed by plate tectonics.

Since the question specifically asks for a formation that does not rise at least 1000 meters, the only option is a seamount.