In astronomy, "satellite" was first applied to celestial bodies that orbit planets. This is because they are like attendants to the planets, moving around them due to their gravitational pull. The term "satellite" is used in this context because it captures the idea of a smaller body orbiting a larger one, just as an attendant would follow a leader.
So, the moons are called satellites because they are celestial bodies that orbit a larger body, like a planet. They are essentially the attendants of the planets, following them in their celestial dance.