My sister was put on the house in the event my mother die. I was under age at the time. I could have added my name if my mother wanted to when I was of legal age. It was never suggested that I put my name on the house after I became of legal age!
You haven't provided enough information for me to provide you any specific guidance. I can say, however, that you have no ability to "put your name" on the house. Whoever owns the home at this time is the proper (and only) party that can convey an ownership interest to you.
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