I know there are more of these but I can’t recall them at the moment.
Jane Seymour (born Joanne Frankenberg, took her name from the third wife of Henry VIII).
Anne Shirley (actress born Dawn Paris [a good name in and of itself for an actress] who changed it to Dawn O’Day and then changed it to honor her character when she starred in Anne of Green Gables).
Paul Revere of the group PAUL REVERE & THE RAIDERS really was born with that name, though his name at birth was Paul Revere Dick. He sliced it off to go into show biz.
Who are some others? I feel I’m missing someone really obvious.
Tom Jones is the first to spring to mind. (Born Thomas Woodward, he was given the name Tom Jones, because his image was similar to the character of that name.)
Half his name - David Bowie was born David Jones, but since Davy Jones of the Monkees was performing as well and this created confusion, he picked the last name Bowie after Jim Bowie and the Bowie knife.
I don’t know if Jesse James of West Coast Choppers counts as an entertainer, exactly, but he did use to have a TV show where he customized cars and whatnot.
Not an entertainer, but author Adam Smith, best known for his books on economics, took his pen name from the original Adam Smith, a philosopher of economics.
Adding to the list of rock group names, there was H.P. Lovecraft.
Bob Dylan took his stage name from poet Dylan Thomas.
Bit actor Fred Asparagus most likely took screen his name as a play on Fred Astaire.