FTM has a "fact" called adoption. This is the usual way of expressing when and where the event took place. You also modify the relationships between the child, the biological parents, and the adoptive parents in the relationship tab of the people workspace.
As for names that you display to other users, that's your call. Most genealogists use someone's name at birth as the preferred name fact. There is also an AKA fact that can be used to capture nicknames, changed names, etc. It's your call which you want to be preferred and which to be the AKA.
As for names that you display to other users, that's your call. Most genealogists use someone's name at birth as the preferred name fact. There is also an AKA fact that can be used to capture nicknames, changed names, etc. It's your call which you want to be preferred and which to be the AKA.