Ned Alleyn is played by Ben Affleck. We mention this because whenever he is on screen, you think, "That's Ben Affleck. Why is he in this movie?" Gwyneth gets a pass because she thinks she is British, but Ben Affleck? The Boston boy is far from home in this film.
Critique of the casting aside, Edward Alleyn is a real-life historical figure who looks nothing like Ben Affleck.
In the film, he is the founder of the Admiral's Men, a prestigious acting troupe. He is the big name Shakespeare needs to put on a successful play, and Will gets him to sign on with a little bit of deception. Will tells Alleyn the play is titled Mercutio… which is who Alleyn agrees to play.
Before you feel bad for him being duped, remember: this guy is full of himself. "Pay attention," he says. "You will see how genius creates a legend." Throughout rehearsals, he's kind of a jerk, but because of him, Mercutio gets some of the plays more memorable lines ("A plague on both your houses!") and a juicy dramatic death scene.
Will writes these scenes for Ned to keep him happy, and Ned comes around in the end, approving of the play because it's just so good, even if he is not the star.