Mike may have had an emergency of his own which required that he shed his coveralls in a hurry.. So if he was working on the beetle when the call came, that's where they got stashed... Or Harry may have bought them at Good Will because they fit, to keep in the car for emergencies when he finds he has literally nothing to wear. So the name tag "Mike" is just a coincidence that it happens also to be the name as his mechanic.
One thing to keep in mind, Harry is six foot nine, so unless his mechanic is also at least six foot five or so, heavy coveralls aren't going to fit because they do not stretch.. Yes, coveralls have some give but it is usually to accommodate expanding middles as opposed to heights.