There are plenty of tennis competitions named 'open' such as the French Open, Australia Open, or Mexico Open.
Is there any particular reason for this naming?
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Before 1968, only amateur players were allowed to compete in the four tennis Grand Slam tournaments; professional players had an entirely separate set of tournaments.
"Open" refers to the state since 1968 where both amateur and professional players can enter the same tournament. Of course, the skill level is such that realistically it is only professional players that ever even get close to winning tournaments, but in theory an amateur player could enter and win.
See also golf - e.g. the British Open and the U.S. Open; the "open" naming is exactly the same there as opposed to the PGA Tour which is open to professionals only.