Congrats bro and good luck to ya. I was thinking something like "Cellular Enterprise" go global with it son... or "Everything Cellular!" "Dash's Mobile Enterprise" .. man...too many to choose from. This is a good link to check out on ways to come up with a good name for any company or new business.. check it out..
Code
http://www.yudkin.com/generate.htm
other than that, I think what will make your store different and what I would make note of and focus on is the modifications and unlocking etc you will offer that you can't get anywhere else in store. I mean there are a couple places here in Jax, Fl that unlock phones and stuff and sell used phones but you don't have to do much to be different from cell companies because none of them offer unlocking or themes or any of that really so I would make that be the highlight of services you offer that "those other guys" don't. Well I wish you the best and will put my thinking cap on and see what I come up with, I haven't put much thought into it I just happen to see the post so until then I'm sure you have a few ideas to choose from. That link makes a lot of sense though so you might want to check it out before your final decision.