"Science Made Stupid" had a wonderful cartoon showing the three basic models of the Universe.
Heliocentric: everything goes around the Sun.
Ethnocentric: everything goes around your nation (the cartoon depicted China).
Egocentric: everything goes around you (cartoon showed the planets and Sun revolving around a smiling person's head).
Regarding what to call the two hemispheres of the Moon.... Astronomers call them the nearside and farside, of course, but residents of the Moon might use different words. I once tried to write a story about a race of creatures living on Titan, Saturn's largest moon. (Unfortunately, I had a problem developing an actual plot, so it went nowhere and was ultimately abandoned.) Titan is also synchronous with its parent, always presenting one face towards Saturn. For the story, I referred to the Saturn-facing side as the "topside", as the native people's ancestors had believed Saturn to stand over them, and believed that the point with Saturn highest in the sky (the point nearest to Saturn) was the highest point on all of Titan. The "lowside" was the side facing away from Saturn.
A really curious situation is Pluto-Charon. They are *mutually* synchronous, so not only does Charon always face on side towards Pluto, but Pluto also faces one side towards Charon. Thus, a person standing on the inward side of either would see the other one fixed motionless in the sky, going through phases while the stars wheeled endlessly by behind it (along with Nix and Hydra, of course, which aren't in the same orbit as Charon and probably are not synchronous with either body -- I would expect that gravitational influences of Pluto and Charon acting on both of them would prevent them from settling into synchronous rotation).