"Der zur Sonne hin geht" is very literally, but it sounds pretty much O.K. for me too. It also lacks the English "-tender"-conotation, while my 'den es zur Sonne (hin) zieht' is probably a little bit overinterpretated. Most native American names I have heard in German did NOT sound this way. The were like "Fliegender Adler" (flying eagle). Plain and simple.

I tend to associate longer constructions as names in German with Central/South American indians or maybe those in the Himalayas.

Sonnen-Geher is nonsense, like солнцеход or something. It's way tooo literally, without any preposition. OK, in Russian you could probably name a solar vehicle солнцеход (<- луноход), but in German it is just pure nonsense.

@Rtyom
Do you speak any German?