I have also seen this called Mary at the-athenaeum.org and artuk.org (where this image came from), but thepeerage, geni.com, and the UK National Trust Web site refer to this as a portrait of Margaret Spencer. According to geni.com there were two Margaret Spencers born in 1627 - this Margaret who died in 1704 and another Margaret who was Countess of Shaftesbury and died in 1693.
From artuk.org.
She has a sheer modesty piece above a sheer bertha and has a wrap pinned with clasps like a second bertha.
Keywords: 1662, Margaret Spencer, Mrs. Robert Lucy, Baroness Arundell of Wardour, Spencer family, Lucy family, Arundell family, Baroness, British, hurluberlu coiffure, hair jewelry, earrings, necklace, split modesty piece, scoop neckline, brooch, fitted bodice, bertha, off shoulder scoop neckline, wrap, clasps, quarter length slashed upper sleeves, arm bands