Polly is an English diminutive of Molly — itself a diminutive of Mary (from the Hebrew Miriam). The shift from M to P followed an old English pet-name pattern (Megan → Peggy, Margaret → Maggie/Peggy).
Polly was hugely popular in 18th and 19th-century England. The character Polly Peachum in John Gay's The Beggar's Opera (1728) gave the name early literary fame. Today Polly is returning fast as part of the vintage revival.
Polly reduces to seven — the number of warm familiar grace.