The AP article also indicates that the derisible name was given by the team's first owners, the Walt Disney Company:
The Mighty Ducks were formed as an expansion franchise in 1993, and named by then-Disney chairman Michael Eisner after the company's movie of the same name.
That "movie of the same name," of course, was the forgettable live-action hockey movie starring Emelio Estevez. At least, it would have been forgettable, if Disney hadn't shamefully named a professional sports franchise after it. What a travesty. The team is under new ownership now, and this move seems to demonstrate a desire to be taken seriously.
The Ducks' Major League Baseball counterpart, the formerly Disney-owned Angels, recently took a similar step. They were the California Angels before Disney bought them and renamed them the Anaheim Angels so as to include the title of their pretend city. New ownership moved slightly away from that and renamed the team the Los Angeles Angels of Anaheim, which of course just gets shortened to the LA Angels, which of course is what it should be in the first place.
I dunno, it's late and I'm apparently grumpy or something. But the point is that Anaheim and Orlando are stupid and not real places, naming a pro sports team after a kids' movie is foolish, and it's better that Disney just keep its hands off stuff that matters. I can't wait to see how they screw up Pixar. Yeesh.
UPDATE: It turns out the city of Anaheim is suing the Angels' new owner. If that interests you, read the article here.