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I think this is much more than a "guess". The only "unknown" part to the equation is why it was "P" that became the sound chosen to form the rhyming form. But it is quite clear how Margaret leads to Marg which leads to Mag which leads to Meg. And the final step to Peg -- well, we know that it was quite common to create rhyming forms of nicknames of other common given names in medieval times, such as Hick and Dick from Richard.

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Both Peggy and Polly have been in use since the early 1200s. And we also have Patty, in use as a pet form of Martha since the late 1600s at least. So it just became the custom for common female names starting with M to develop rhyming forms with P.