Yes Native Americans are still given names. It is done by a Medicine Man and only after he has met the individual and received a vision.
The local medicine man in my part of Northern Michigan is Chippewa but the locals prefer the Lakota man who travels through here several times a year.
Interesting to me is that there are no longer any "Man afraid of his horse" or " Little Big Man" Every one now seems to be Bear, Eagle, or Wolf something or other.
thanks, mustard plaster. your knowledge seems to supercede mine. i respectfully retract some of my animosity toward name callers.