My DF wants to adopt my daughter. Is this possible, when she goes to her father every second weekend?

Also, is it possible to change her surname to add DF's? She's Possum Smith, and I'd like her to be Possum Jones-Smith, as Jones is DF's name, and will soon enough be mine too. So we'd be Echidna Jones, Wombat Jones and Possum Jones-Smith.

(sorry for the aliases, I like being private here.)