I wear the tartan of my surname, usually the hunting version because I like it better.

If I see someone else wearing the same tartan (rare but it has happened). I would certainly make a point of speaking to them.

If we shared the surname I would be pleased and discuss potential blood ties.

If they said it was because of their Great Grandfather on their mother's side I would still be pleased but less interested in seeking a blood relationship which is so far removed.

If they said "I just like the colours" I would be mildly miffed but certainly not enough to say anything unkind. I have no rights of ownership of the tartan any more than I would a street called my surname. (Unless it was named for me but I have yet to do anything notable enough for that.)