No you don't. Not in english at least. The moon or sun is understood in context and with the article "the". "The moon" and "the sun" without qualifications is understood to mean earth's moon or earth's sun. General references like "a sun" or "a moon" connote non-specific and non-identifying moon or sun. If you want to specifically identify other moons or other suns, you qualify it like - the moons of jupiter or sun of X solar system.
As an example, the recent SpaceX announcement.
"The proposed trip—a trip around the moon for two passengers lasting about a week—is almost the same as a scheme hatched by the tourism company Space Adventures, whose president told Quartz last year it had two clients booked for the mission."
https://qz.com/920993/who-are-the-space-tourists-elon-musk-w...