Name changes and adoption?

This is not happened to me, but I am just curious. If a young child lost both of their parents (probably tragically), and the child was then adopted by godparents (or other close family), would the godparents change the child's name to theirs? Or would they keep the child's old last name? I'm sure that this is probably different depending on the adoption, but is there a usual method to this? thanks :)