Does my husband have equal ownership of a house I purchased in my maiden name after we were married?

In 2015 I started the process of obtaining a mortgage. I cleaned up my credit, etc. I finally was in a position to buy a property. Several places fell through but I still had an approved mortgage application in good standing. During the course of this time I got married. I never changed any of my information on my mortgage application. My new husband couldn’t be added to the mortgage because of his credit and a recent foreclosure, so I continued in the same vein I started in...If we divorce, would I be required to split the home with him. He is not on the deed or the mortgage. He wants me to sign a quit claim deed to change the deed from my maiden name to my married name and then add him to the deed. What are my legal rights in this situation?