Not that I know of no you can't. Also won't be the first time I was/am wrong either. If you still have, the filled out form or the gunstore still does, then look it over section by section. If you have a middle initial then spell out the middle name if you haven't allready, Check to make sure the place of birth is correct, and your S/S # is also correct. Other than you may have had your identity stolen and used if everything is correct then I can't see any reason why it would be denied at all. Especially since you have a CCW. After all you had to go through the same checks actually more detailed checks considering your finger prints were processed, so something had happened Possible the clerk gave the agent the wrong numbers and didn't even realize it, or misspelt your name over the phone of the Agent misspelled it.
Other than filing an appeal maybe, possibly, you can stop by the Police Station or Sheriff's Office and ask them if they can do a background check on you. Frankly I doubt that they will, but then again for a fee they ran your prints so maybe they have fees for getting your own background checked. I have no idea what so ever other than what I have just said and that is only a guess on my part. Keep in mind that if your ID was stolen and someone did something to cause theproblem the LEO's might see the issue and then arrest you while you are there. Then again you could ask a Land Shark, sorry Lawyer if it can be done and if so for how much. Hopefully it's someone you know more or less well or at least on a friendly basis and won't nick you for their fee for giving you their advice.