This method should works if your account was already verified by your ID, and Facebook close it back again asking you to change your name or to verify your account back again . Else, please find your suitable form and submit it : Facebook Accounts Support Forms

For many users and after login they will ask to verify their accounts by submit their IDs. Mostly they wont get any reply, this problem showed up at Jan/2015 and it might be solved right now . 

If you face this problem follow these steps : 

1- login to your facebook account email (hotmail, gmail ... etc) 

2- Search your inbox for "support.facebook.com" 

3- Send a new email for all the emails you collect from step 2 : 

Subject : verify my account 

Message: Hi, i already verified my account with my ID, please remove the restrictions . thank you . 

Remember you also should use the suitable form to verify your Facebook account by reading this article : Facebook Accounts Support Forms