Greymantle was a title borne by two famous characters in Tolkien's works. The first of these was Elu Thingol, the King of Doriath in the First Age. His Sindarin name Thingol (and its older Quenya equivalent, Singollo) both meant 'Greycloak' or 'Greymantle'.
The name reappeared in a quite different form in the Third Age, when it was one of many acquired by the Wizard Gandalf on his journeys. It was said to come from a name given to him in the Westron or Common Tongue. That original name was possibly Incánus, translated into the language of the Rohirrim as Greyhame, and so into modern English as 'Greymantle'.