Strange, I often rename their capital to Mexico City when I take it. I can't stand the Aztec names, they look too similar.
I think it's better to choose your opponents on TSL map, as obviously Greece and Macedon can't start next to each other. I just finished my first game as Macedon as well. Funny I didn't even realize they released 2 civs at once, I thought we only got Persia (which I played last week). I had barbarians on which makes a HUGE difference. Compared to last game where I was worried about losing (I had barbs off that game), this game I never even came close to losing. I gave North and South America to America, but with barbs on they never did much. All other civs were old world civs.
Even on Epic speed the usefulness of their units lasted plenty long enough. I'm not a big fan of their unique building though. Seeing as one of their unique units is a mounted unit, and I'd like to build stables. I ended up building 2 encampments, one with a stable, and the other my unique building. I conquered Russia, Persia (who had quite a few cities) and finally Spain. Spain actually turned out to be the hardest. I tried them early before I conquered Russia, but I didn't have enough units to overcome their archers (who were behind Madrid and I had a hard time getting to them without being pummeled and having to retreat). I finally got them the second time, but even that wasn't easy. I ended up using catapults since the siege tower wasn't enough at this point.
Had control of all of Europe, Iran area, India, and Indochina. Wasn't in the mood for another global conquering game, and just peaced out after that and went for science victory. My war monger status managed to degenerate, and I was able to form alliances with 3 out of the remaining 4 civilizations.