Can I be sued or evicted for using someone's name legally?

My mother married my stepfather 25 years ago, and at that time, he did not legally adopt me. However, he has acted as my father ever since, and all my documents list his name as my father. After his passing, his family is threatening to sue me for using his name in my legal documents, as they are after his property. They also threaten to kick me out of the house. Is it possible for me to get arrested for using his name as my father, and can his family kick me out of the house because I was not legally adopted? Please answer, I am in a really tough situation.