A wild speculation: perhaps Moon is the huge asteroid that hit and liquefied the planet that was there before Earth, so some of its material sticked to that asteroid and formed Moon, while the rest formed Earth. In this case, the two sides of Moon show the direction of the impact.
I mean, the prevailing theory is that the Moon formed in the aftermath of the Theia–proto-Earth collision. Indeed the existence of the Moon is why the Theia hypothesis was proposed in the first place. But the bulk of Theia’s mass (which would have been ~10% of Earth’s mass) is thought to have mixed with Earth’s and sunk into the core/mantle, while most of the Moon is made of same material as the modern Earth’s crust.
However, the differentiation of the Moon’s near and far sides must have happened later, presumably during what’s called the late heavy bombardment (“late” is relative here; we’re still talking ~4 Ga ago). Although I believe some recent research has cast doubt on whether the LHB actually happened at all.
