Matt,

How are you that eloquent so early in the morning? Well done indeed, sir!

Since Gibson is considered part of clan Buchanan, then that is your clan and if you are going to show loyalty to the clan, you need to display and wear that clan cheif's crest badge. It doesn't matter is his last name is different than yours. (As a side note, Buchanan, I beleive, does not have a cheif at present, so displaying the cheif's crest as a badge would not be a display of loyalty to him as a person, but rather to the position of the chief should it ever be filled, and of course to the clan itself).
I can confirm that the Buchanans have no chief at present, thanks to a friend of mine who represents the Clan Buchanan society in Louisiana at present.

Cheers,

Todd