To chip in a couple of historical notes: K Henry VII (the great-grandfather of Queen Jane Grey) was a Tudor not a Stuart. It was through his daughter Margaret Tudor, Queen of Scotland, that the Stuart king James VI and I (Queen Margaret's great-grandson) inherited the throne of England.

At some point, I expect in the 19th Century, the Royal Stewart tartan became a universal tartan, as did the Government Sett (known universally as the Black Watch tartan).

As someone pointed out, in naming one is the son/daughter of one's father. However, it wasn't and isn't that simple in the Highlands and Islands. You can also be known as the son/daughter of your mother, or even your grandmother. It was all a simple and handy way of identifying someone in smallish communities by picking on something that was well-known in that community. I'm still known in certain circles as "David Isla Jean's son" (and a second cousin is "David Muriel Jean's son").

One can belong to a clan by descent, area affiliation, or election - you can decide (elect) to affiliate, for whatever reason. Traditionally one would have to approach the clan Chief. Nowadays, it's becoming more common to find people who just decide that they're going to be part of that clan and carry on as if they were. Of course, if one wants to join the clan society/association, then one would probably have to go through the clan Chief.