Legal issues for child hindu muslim marriage

I am muslim woman married hindu man one year before and my marriage is happened as by nikkah... my man converted to muslim for the sake of our marriage to convince my family and for nikkah....and after that we r not facing any difficulties in families....and we r happily ran our marriage life.... But he wants to back to their own religion... even he is not having any belief on any of the God. ... only he wants to go back for retain his old identity and mainly for his old name.... First question is if he reconverted to his old religion means , do we have any legal problem in our marriage...I mean still our marriage is valid legally.... Second question is we r decided to give his old name to our child birth certificate...is it make any legal issues...since still he is not reconverted and as per gazzet he is carrying new muslim name.... I want the legal advices.....