This is a bit of a difficult question.
In Renaissance Italy, how would one's name change if they were adopted?
For instance, my character is Adelina Disertore. If she is adopted by Facesco Basso, and wished to take his name, how would that work? Would she simply become Adelina Basso, or is there any specific way that it works?
Answer on How would the name change if someone was adopted?
You question is not at all difficult, when adoption occurred the surname of the adoptive family would be used as the name of the adopted. So Maria Como adopted by the Francisco family would have simply become Maria Francisco. In a book or story, from Renaissance Italy, there may have been a service performed in the Church and the adoption recorded there, but there is no know n specific civil procedure or formal recording of the adoption. In Wills the person might have been referred to as my adopted daughter Maria Como Francisco.