From what I've seen, either name is fine o.o; But on the show, they (the Keroro Platoon) don't say 'chikyuu' in reference to Earth.
They say Pekopon..~
I think the name of the song is incorrect. The closest one i can find with a similar name is "Omatase Chikyuu Icchou!" (ãŠã¾ãŸã›åœ°çƒä¸€ä¸!), which is also the name that animenewsnetwork calls it.
Source: http://www.animenewsnetwork.com/encyclopedia/anime.php?id=3711