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It was all a lie. Michael ANDREW Fox had to change his name because two people can't be registered under the same name in the Screen Actors Guild. (There was someone already registered as Michael Fox, so that's why he added his middle initial in the first place.) He didn't like the name "Michael A. Fox" because it sounds literally like "Michael, a fox," so he went with Michael J. Fox, in tribute to actor Michael J. Pollard.
2.
Meryl Streep was born Mary Streep.
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Her birth name was Mary. Her father "made up" the name "Meryl," so she went by that that. Meryl apparently hated her father's nickname and wanted to be called Patty or Cathy.