I want to pitch in a note on "septs." Matt has said it VERY WELL.
There are some "septs" that are PERFECTLY legit. The name itself is rare and comes from a family that held a hereditary office in particular clan, so was distinct from the normal clansman WHILE tied to THAT particular clan, but NOT the "chief-line" either.
On the other side, some "septs" stretch in imagination. Matt mentioned a number of these. It seems that, during the popularization of "clan tartans," some enterprising person went through the Scottish surname list and simply scattered all the unassociated names with A clan.
So, one should be cautious in over-claiming through a "sept" (such as getting a HUGE tattoo that covers your back) without any real research.

So, what is the PRACTICAL implication?
One of my "family names" is Todd. Todd is pretty closely associated with Gordon and is usually just said "Todd IS Gordon." "Todd," itself, comes from "Fox" (I've been told). Now WHY Todd is associated with Gordon is something I have not been able to establish. So, I WILL be making a kilt in Gordon. I would have hesitation in getting a Gordon tattoo, though. I happen to REALLY like that tartan, so that's cool.
Another name is Wilson, which is generally associated with the Gunns. Wilson is probably one of the MOST common names in ALL SCOTLAND. There is, however, a REAL reason for the Wilson association with Gunn (and several versions of precisely WHY). So, many Gunns are Wilsons, though most Wilsons probably are NOT Gunns.