Yes, the names given to Native American tribes by the US Government, especially the Sioux, should be reexamined. For centuries, the original inhabitants of our country have been subjected to various atrocities. At the least, Native Americans tribes should be given sovereignty, or at least the ability to weigh in, on what they are referred to.
It is perfectly reasonable that Native American tribes should be allowed to make their own decisions about their official name. It is not necessarily going to be the case that all tribes will reject their given names but if some feel strongly about the issue the they should be given the option to assert their will.
If a tribe wants to take issue with its name (for any reason) it clearly is within it's rights to do so. Being aware of our history can lead us to the awareness of the sources of these names and that may be troubling. If the name is truly negative in it's origins or it is from an oppressive force as the government had been towards the Native Americans then it should be reexamined. This process can help the people take back their identity and strengthen it's community.
No, the names given to the Native American tribes by the U.S. government should not be reexamined. The names that were given to them are recognizable and set. It would be appropriate to also recognize the original or more accurate names, but a complete change would be confusing and expensive and generally unneccessary.