Black's "Surnames of Scotland" gives "Straughan" as a variant spelling of "Strachan" a locational surname from Strachan in Kincardineshire and dates the first appearance of the name to c. 1200. (George F Black; The Surnames of Scotland; New York Public Library; 1946.)
I ran a search on familysearch with dates 1600-1700 and came up with some earlier Straughans. Predominantly Northumberland and Durham, but some London.
Scotlandspeople has about a dozen Straughans in the late 1600s. Roxburgshire and the Lothian area which would make sense as possible roots for your north Northumbrian folks. There was a lot of movement down into Northumberland around that time, often following the drove roads.