Linton is of Lowland Scots (and sometimes English origin). It can be derived from a variety of topographical sources: 1) From the Gaelic word linne meaning 'pool' or 'channel'. From Anglic lint meaning 'flax'. 3) From the River Lynne (itself from Brythonic Llynn meaning 'torrent').

Since this is a series of unconnected names, I would say they are not a clan or even a sept. (Except maybe in a 'convenient' modern sense, like in a tartan shop.) A district tartan would probably be a good idea. It could be one from a region in the Lowlands of Scotland or perhaps even County Derry, Northern Ireland.