Changing one's surname

I was born without a father. He took off before I was born. I only saw him once, I was 16 years old then. No financial whatsoever. My mother raised me alone. They were married but the marriage was annulled when I was 8. We live in the Philippines where Democracy is the law. We are Moslems but because of my father's absence while I was growing up, I was given a surname that is of my mother's. I know its not permissible but I was a kid back then. Now I have my own family. I need to file for my children's correct birth certificate. I ask authority that if its allowed I'd have my husband's name and last name as their middle name and surname respectively. However, our government doesn't allow things like that. I know in Islam it is not permissible to attach the surname of your mother to the names of your children. But our government requires us. Now, my problem is, if I have to attach my surname as their middle name, am I somehow commiting a sin? Using my wrong surname(my mother's last name) as their middle name is a sin already but the fact that it is a wrong surname makes it even more complicated. I cannot just change my surname because of some pertinent documents. If I do, my children might not be able to receive whatever our government has to offer them thru me. Should I just let them use my surname as their middle name since even if I change it to my original surname (my father's), it doesn't make it right in Islam. Allah Ta'ala knows, I tried convincing them, citing that in Islam children are supposed to bear their fathers name and surname but they won't let me. Please help. I am going to send my kids to school but their records are not set right.