Based on the credit lookup tool, and the fact that IMDB uses single quotes ('Red Crow'), I'd say that Floyd / Red Crow / Westerman should be the "common name", and Floyd Westerman should be the "credited as" name.

Also:
http://www.nativecelebs.com/profiles/floyd_red_crow_westerman.htm
and
http://en.wikipedia.org/wiki/Floyd_Red_Crow_Westerman
and
http://www.nativepeoples.com/article/articles/1/1/Floyd-Red-Crow-Westerman/Page1.html

I did a little research with the Credit Lookup Tool and in comparison to the (as )-entries in IMDb he seems to be credited at least in his bigger films (Dances With Wolves, Hidalgo and The Doors) and in many of his X-Files appearences as Floyd Red Crow Westerman.

So if in the future most of the IMDb data will be corrected in the Invelos database the majority of his profiles should have him listed as Floyd Red Crow Westerman.

In my opinion Floyd / Red Crow / Westerman [Floyd Westerman] is the correct one to use.

mfg Speedy