You don't have an Indian name unless someone gave you one. Rather than thinking about the name, perhaps you would enjoy learning about the Cherokee people. I'm sure that there is a lot of information out there. Having a name won't make you feel closer to your roots, but understanding who those roots were might.
observe your tast ... if you prefere kraut so you are a lot german, if you tend more to potatoes you´re most irish but if your tast is mor exotic you´ll be most indian ... ;-)
Check back through the official birth records.
You'll be able to work out the percentage, when you know how far back the Cherokee antecedents are.
I know very little about Amerindian cultures.
You could travel to a place where lots of Cherokee live,
and where a community is still keeping its traditions alive.
I'm guessing that if you prove yourself worthy, you might be allowed to train for initiation.
I believe in your final initiation
you will be put in a situation that allows you to discover your spirit name.
The community might decide to give you a tribal name, although there could be conditions.
Don't trust New Age commercial programs that ask money,
but do be prepared to give back to the community in full value.
Check the phone book you must be in there some where! Like I said check some where but not sure if EP is going to help! lol