Yes indeed. Turpin's and Riverkilt's replies echo my own thoughts.
On Ulster Scots, my mother's family were Northern Irish Mewhorts. It is known that they were originally granted a plot of land near Lurgan in 1691 where a cottage was built which was in the family for over 200 years. The original Mewhort is believed to have been a McWhirt or McWhirter from Ayrshire Scotland who modified his name to blend in better with the native Irish. On my father's side, Cunningham, I am pure Scottish, though the surname is now very common in Northern Ireland where many Scots Cunninghams settled and in Ireland there are the towns of Manorcunningham and Newtowncunningham. Through Clan Cunningham I have met a few American based Cunninghams whose ancestors crossed the Atlantic from Ireland, no doubt if they could trace far enough back they would find an original Scottish ancestry.
Addictive, certainly, for every generation you go back the number of ancestry lines to research doubles!
Best of luck!