What is the name for a black hole whose mass is millions to billions of solar masses?

A black hole with millions to billions of solar masses is called a supermassive black hole.

Supermassive black holes are the largest established black-hole class, with masses ranging from hundreds of thousands to billions—or, in some cases, tens of billions—of Suns. Observations indicate that nearly every large galaxy has one at its center, although the evidence is much stronger for some galaxies than others.

The Milky Way’s example is Sagittarius A*, a roughly four-million-solar-mass black hole at the Galactic Center. When gas spirals into a supermassive black hole, friction and compression can release enormous energy, powering an active galactic nucleus or quasar.

The name describes mass, not visibility or activity. A dormant supermassive black hole may produce little light, while a much smaller black hole can appear extremely bright if it is rapidly accreting matter. The Event Horizon Telescope has directly imaged the shadow-like surroundings of Sagittarius A* and the supermassive black hole in Messier 87.