I'm married but I intend to file a divorce with my husband soon. Is it possible for me not to add his name into my child's birth cert? I'm afraid he would snatch my son from my if we divorce. Someone please advise.

if you are not puting his name in the birth cert that mean the child is born without a father. I know child under 15 is under mother custody. But still if your husband having a lawyer to have that custody he need to have divorce first for a three years separation and carry on the custody.