Damaris was born at Plymouth Colony say 1628 to Pilgrims Stephen & Elizabeth (Fisher) Hopkins. She married Jacob Cooke at Plymouth shortly after 10 Jun 1646. Since this Damaris was still bearing children in the early 1670s, she cannot be the same Damaris who came on the Mayflower. Source: Anderson's Pilgrim Migration
Find A Grave contributor William adds, without citation: She was born 22 May 1627, and died 18 Nov 1669.