There once was a young actor named Michael Douglas. He had to change is name though, because there already was the Michael Douglas. He changed his name to Michael Keaton, inspired by actress Diane Keaton, who's real name is Diane Hall. The film that's about her is called Annie Hall and it's by Woody Allen, who's real name is Allen Stewart Konigsberg.
I also like the Sheen - Estévez family.
Martin Sheen - Ramón Antonio Gerard Estévez
Charlie Sheen - Carlos Irwin Estévez
Emilio and Renée Estévez decided to stick with their real name while brother Ramon Estévez is also sometimes billed as Ramon Sheen. He runs a production company called Estévez Sheen Productions.
Also: Joaquin Phoenix used to be credited as Leaf Phoenix as a child, because he wanted to have a nature-related name like his siblings. He changed it back, though.