There aren't many places where names are first come, first-served, but actors' unions are one of them. If you tried to register with one and found that someone was already actively using your name, you'd simply have to pick another one. It's likely not a problem for people called Gyllenhaal, but the 10 entertainers below had slightly more common names.
1. Michael Keaton. The name on his birth certificate? Michael Douglas. I guess you know who got to that one first. (Beetlejuice is my favorite Michael Keaton, by the way.)
2. Michael J. Fox. Michael Fox was already spoken for, and the future Alex P. Keaton didn't want to use his real middle initial, Andrew - Michael A. Fox was just too ridiculous. He decided on "J" as a tribute to actor Michael J. Pollard.
3. Nathan Lane. Though he went by Joseph through high school, Lane discovered his name was no longer an option when he went to get his SAG card. In true Broadway fashion, Lane chose his first name based on Nathan Detroit, a character in Guys and Dolls.
4. Stewart Granger. British actor James Lablache Stewart wanted to register as James Stewart, but it was already taken, obviously. He kept his last name, but dropped the "Jimmy" and added "Granger," his grandmother's maiden name.
5. Terry O'Quinn. Sometimes it just takes a little change to make a difference. In O'Quinn's case, he simply added the "O" after discovering "Terrance Quinn" was already used with Actors' Equity.
6. David Tennant. Fans of Doctor Who know this actor as the 10th Doctor in the series. But he only took his Neil Tennant-inspired name after finding that "David McDonald" was already on the books.
7. David Walliams. Another clever way to circumvent the system is to simply substitute a letter in your name. That's what David Walliams did. I'll let you take a guess at his real surname on your own.
These three people weren't required by any actor's unions to make a name change, but you'll see why they did.
8. David Bowie. He had been rocking by the name Davy or Davie Jones, but if you were David Bowie and were trying to create the David Bowie image, you'd probably get irritated at people asking what happened to your career with the Monkees as well.
9. Katy Perry. Born Katheryn Hudson, Katy chose to go by her mother's maiden name when she started to get popular so she wouldn't be confused with actress Kate Hudson.
10. Albert Brooks. Though it was probably a good conversation starter, Albert Einstein changed his name to Albert Brooks when he started acting. Bob Einstein, his brother, kept his surname - but you probably know him better by his stage name, Super Dave Osborne. Bob is also Marty Funkhouser on Curb Your Enthusiasm, and as my Twitter followers already know, finding out that Super Dave and Marty Funkhouser are the same guy kind of blew my mind.