What is the cluster of galaxies called?

Answer 1

Vast groups of gravitationally bound stars (typically billions of them) are called galaxies. Smaller clusters of stars (up to a few million) may be called globular clusters.

Each galaxy may have a proper name. For example, our galaxy is called "The Milky Way." Our sister galaxy is "Andromeda," after the constellation near which it appears in our sky. (The constellation stars are nearby--at most a few hundred light years away, whereas Andromeda is over 2.5 million light years from us).

Answer 2

The general name is "galaxy cluster". The specific galaxy cluster in which we are located is called the "Local Group".