Emigh Family Genealogy Forum
Yes, it does appear that the names are related. In studying the Beekman Patent, Duchess Co., NY data I have encountered Emig, Emigh, and Eighmy.
Unless I'm being steered in the wrong direction, There appears to be a change in family spelling in the course of two generations. A genealogy prepared by my Great-Grandfather (Black) notes descendency from Jeremiah 'Emeigh' (b. 1754)et al from Beekman Patent, down 3 generations until Louisa Emeigh married George B. Allen.
To see more info on this family line see the post on Michael Emeigh elsewhere on this surname forum.