What is the name of the homeworld of the Betazoids?

The homeworld of the Betazoids is Betazed.

Betazed is a planet in the Star Trek universe and the native world of the Betazoid species, a people famous for powerful telepathic abilities. The planet is associated with lush scenery, distinctive cultural traditions, and a society in which mental sensitivity is treated as an important part of everyday life.

The best-known Betazoid is Deanna Troi, the Enterprise-D’s half-Betazoid counselor in Star Trek: The Next Generation. Her human father, Ian Andrew Troi, and Betazoid mother, Lwaxana Troi, help explain why Deanna can sense emotions more strongly than ordinary humans while not always possessing the full telepathic range of a Betazoid.

Betazed is also a member of the United Federation of Planets. It is sometimes confused with Vulcan, Romulus, or Andoria, but those are separate worlds belonging to other major Star Trek species. Betazed specifically identifies the civilization and homeworld connected with Betazoids.