My original reply posted before I finished and now I can't figure out how to delete/edit it! So here's the finished reply. Sorry for the confusion.
I think I saw that you already got an answer that works for you but I ended up having to do this today so I'm posting this to help anyone else who might have a similar issue!
Ashley
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How to change the name associated with an Apple ID:
1) In iTunes, select Account from the menu bar at the top of the screen and choose View My Account from the dropdown - it will prompt you for your Apple ID and password


2)Select Edit at appleid.apple.com (<--- OR GO THERE NOW) and Sign In


4) Update the details that you would like to change by selecting Edit


5) Select Done!
6) Plug your iPad into iTunes and select Account to verify the changes were successful.
If not, log out and back in once more.
If it's still not changed, repeat the edit at appleid.apple.com and make sure to mark done to save the changes.
If it's still not changed after that??? I'm not sure at that point.
Good luck!
Other notes:
One might have an incorrect name for a handful of reasons (list not exhaustive)
- It was set up incorrectly
- You changed your name
- You shared an Apple ID with someone at some point
- Someone gave/sold the device to you and it's still under their details
- An ****** changed it in to fulfill their lifelong dream of being an ******
If the device is under someone else's Apple ID and they gave/sold it to you or you changed your Apple ID and need to re-log into your device, you'll need to log out and log back in with your correct credentials. Go here for other details: What to do after you change your Apple ID email address or password - Apple Support
Also note, I believe anything purchased or downloaded under the incorrect Apple ID will have to be repurchased/downloaded once you sign in with the correct Apple ID but I'm not 100% on that.