Not at all. The noun 'moon' can refer to any, well, moon (like Deimos or Europa). To distinguish between those and our moon, you can use the proper name 'Moon' (capitalised) or Luna if you are so inclined.
The same goes for the Sun. Our sun is either proper name 'Sun', or if your prefer Luna above, Sol. Any other star with stuff orbiting around it is just another sun (noun).
The same goes for the Sun. Our sun is either proper name 'Sun', or if your prefer Luna above, Sol. Any other star with stuff orbiting around it is just another sun (noun).