I was married to my husband in September and got pregnant immediately after. He thought the baby was someone else's and he accused me of zinaa without any witnesses and kicked me out over a month ago. I moved back home with my parents in a different state. Since then I have had little to no communication with him. He is not supporting me and my unborn child financially. He continuously slanders my name, threatens me and emotionally abuses me. I know that under the Shari'ah law he is obligated to financially support me until I have my child. However, in his mind he is not my husband anymore. He said, "I will exercise my right to divorce" through a text message without witnesses but it was never said to my face. I do not wish to see or speak to him ever again. How would our divorce go if we don't even have contact with each other? Also, neither one of us has Muslim family and neither one of us has legally changed our names. He goes by an Islamic name which doesn't have his father's lineage (he got the name from a Muslim woman he calls Ummi that isn't actually his mother) and his legal last name comes from his mother. Since neither name that he has contains his father's lineage which last name would I give my baby? Would it be haraam for me to give the baby my last name since he's denying that he is the father?
Very sorry to hear all this. As far as the divorce issue is concerned, if you do not want to remain his wife you can just ask for divorce and file for it legally. A court settlement will also take care of your and your baby's expenses.
However, you must name the baby by adding his actual father's name -- because however much your husband may deny it, he is your baby's father.
Aside from this, if you think that you want to prove your innocence before the society (for this case may become public knowledge), you can challenge your husband to go for a DNA test to prove you wrong