Terry, you have asked about the history of the name Morgan. I will assume you are talking about the Morgans of Irish (rather than Welsh) origin.
In Ireland, the name goes back to the Irish Gaelic surname Ó Muireagáin, meaning 'descendant of Muireagán' (a diminutive form of some name commencing with Muir...). It was the name of one of the chief families of Teffia, in the present counties of Westmeath and Longford, and sometimes lords of that district. About the beginning of the twelfth century, they apparently dispersed to other parts of Ireland. In the 16th century, the name was most common in Down and Armagh.
The name was variously anglicised O Murrigane, O Moregane, O Morgan, Murrigan, Murricane, Merrigan, Maragan and Morgan.