You might want to check out the names Dunmore and Dunsmuir.

See "Lindores Abbey and its burgh of Newburgh: their history and annuls, pp 433 to 436."

In the process of being anglicized from a celtic language, Dunmore has been spelt many different ways. The addition of an "s" to Dinsmore and Dunsmore comes from the anglicisation of the possessive "'s". In records of the 12th, 13th and 14th century, the name is often spelt Dundemore, which again is a frenchification of the possessive "de".

The name appears in the Ragman Roll as Dundemore.

The Dunsmores, Dunmores and Dinsmores appear to have been relieved of their lands in Fife by the Catholic Church and later by the Scottish Crown. This would account for their flight westward.

I've written some of this up in the wiki page under Dunsmore.

By the way, the names Samual, Robert, John, James and Richard are also in my family. My great-great-grandfather Robert immigrated from Donegal (Antrim) Ireland in 1823. My Dad always told me he was a Scot, and my relatives appeared to have only married Scottish Protestants, so for sure, they're from Scotland and their Protestants.

By the way, Thomas of Dun[de]more was Bishop of Ross, circa 1309, so that might be the source for the first name Ross.