There isn't a specific name for a star and all its orbiting satellites. However, we use several terms depending on the context:

* Star system: This is the most common term, referring to a star and all the celestial objects gravitationally bound to it, including planets, moons, asteroids, comets, etc.

* Solar system: This is a specific term for our own star system, with the Sun as the central star.

* Planetary system: This term emphasizes the presence of planets orbiting the star.

There's no official name for the entirety of a star and its orbiting satellites as a single entity.