As far as I know, no other culture's names are treated as such: the vast majority seem to have their names converted (more or less) phonetically, so Hirohito (Emperor of Japan) is simply referred to as "Hirohito" and not "Abundant Benevolence." Marcus Antonius has become Mark Antony to modern people, but Julius Caesar remains Julius Caesar, and not "Soft-Down Beard." Genghis Khan's name was "Temujin," but I've never seen him referred to as "Iron Man."
Even names that are phrases or poetic nicknames, like "Joseph Stalin", are usually rendered similarly to their native language ("Iosif Vissarionovich Stalin") rather than being translated into something like "Joseph of Steel," even though that was his intent in Russian.
Is there something about Native American languages that makes the translation of their names more accurate or natural than a phonetic rendering? Is it a cultural matter, that their names have some inter-lingual significance that other cultures' names do not? Was there a deliberate choice or commentary on this practice as it was developing?
Or did someone just translate a name one day, and the practice stuck?