Technically, there are no official rules -- it's more etiquette and "how things are done" (and "how things are ignored").
Bear in mind that there wasn't a clear idea of clan tartans until Victorian times. The closest one can come to real rules are the decisions of the Lord Lyon, the heraldic legal authority in Scotland. If you start from the premise that only a member of a particular clan should wear that clan's tartan, the Lord Lyon
has determined that only those who bear the same surname as the chief of the clan (or the surname of a sept of that clan) is recognized as a member of that clan, as is
anyone (and here's the catch-all) who offers allegiance to the chief unless the chief declines that person's allegiance.
These rules are, of course, only binding in Scotland, but even there they are not universally observed, much less enforced. Here in the States, there really are no rules (witness all the Americans who wear the
Royal Stewart), but there will be some curmudgeonly-types who would like to insist on things being done just so.
In my experience, many if not most clan societies in the US (ETA: and elsewhere, sometimes including Scotland) willingly include anyone with the clan surname (or a sept surname) as well as anyone directly connected by descent or marriage to one with a clan or sept surname. With that understanding, your son would certainly be entitled to claim connection to your clan. (And I can't imagine anyone looking askew at him honoring his grandfather that way.)
Mind if I ask which clan?