I was given birth last 2010. Me and my first husband had been together on 2009 and I got pregnant. When I was pregnant we've stayed in my mother's house until I have given birth. My son's last name was followed by his biological father's last name. But when my son was 3 months he was left by his father. Telling that he was going to look for work. We do not have communication after that. Then, earlier 2011 he found my fb account and keep on messaging to come with him in the farm in their province. I refused because it was far from the city and I broke up with him the day he left the house. He would like to take my child but change his mind when I say that I will not go with him. I ask for financial support but he refuse stating that he will not give any support to my child because he is not sure if I will spend it to him.
He promised to visit him but he did not do.

Late 2011, when I met my husband now and we got married April this year. I just want to know if could I file an abandonment case to my previous live in partner? And could we change my sons last name to my husbands last name?

I was living in the Philippines I want to know what was the law process of this case here.

Your new husband has to file to adopt your son. You will need to hire an attorney to prepare the petition.

You don't file an abandonment case, but you can use abandonment to try and push the adoption through.