So if your profile name limit is exceeded and want to change your Facebook profile name to your real name, then
First of all - Click here
Fill that form and you have to upload your valid Government-issued Proof - photo ID like a Passport or Driver's license or any other Document etc and after your upload finishes,
Finally click on "Send" button. Any 1 Proof will be enough in the list of below examples,
Green card, residence permit or immigration papers, Birth certificate Personal or vehicle insurance card Marriage certificate, Official name change paperwork, Voter ID card Non-driver's government ID.
You can submit your College ID card. Facebook staff will verify it and change your name within 4-5 days. So I suggest you to take a clear picture of you proof either by Scanning or by capturing from a good camera or mobile.