In 1602 Bartholomew Gosnold, captain of the vessel the Concord, discovered Martha’s Vineyard.  It was however  already inhabited by the Native American’s know as the Wampanoag’s who called the island Noepe.   I guess they were undiscovered until he arrived.   

Gosnold was taken by the beauty of the island and of the abundance of grapes.   He decided to name the island after his infant daughter.. Martha.  

A popular story is that Gosnold  had three daughters so he named the Elizabeth Islands just west of MV for Elizabeth.. Martha’s Vineyard for Martha.. and the remaining island.. well  ‘Nan took  it’ (Nantucket).  I don’t know if he even had three daughters or if  he did in fact  name Nantucket but it makes for a cute tale.