Clan McCulloch is an armigerous clan, having no clan chief. Forming a clan society does not change that.
In prior times, McCullochs may have chosen their chief by following a commander who could muster enough men to sack the Isle of Man or engage in other daring-do. Sacking the Isle of Man seems imprudent today. Presumably, any descendant of the clan chiefs of Myrton could declare “I am the captain now” and see if anyone follows their lead. Likely on a lark, one member of clan Muir recently initiated a Change.org petition asking for signatories to support his claim to the Court of Lord Lyon to be recognized as the chief of Clan Muir. In reality, it is more complicated than a signature drive. While the Court of Lord Lyon does not actually adjudicate claims to be a clan chief, the Court does adjudicate petitions for the right to use new coats of arms as well as hereditary coats of arms of clan chiefs. When a clan (not a clan society) recognizes a clan chief, that chief may use the hereditary coat of arms of his forebears.
What would a modern Chief do?
The Duke of Argyll, Chief of the Clan Campbel, is the chief of the Campbell clan. As such, he is the owner and keeper of the Campbell ancestral home, Inverary Castle. The Duke of Argyll is also a spokesman for Chivas brand Scotch. The McCullochs retain no ancestral homes. However, if Clan McCulloch recognized a new chief, the clan chief might be able to parlay this into a Scotch branding contract. Maybe.
Coats of Arms
There are traditional rules with respect to the use of a coat of arms. The chief of a clan is the sole owner of the hereditary, undifferenced coat of arms. However, since Clan McCulloch has no chief, nobody is likely to make a fuss if you use the coat of arms from the McCullochs of Myrton that you buy online at a Scottish clan souvenir shop.
According to the Scottish American History Society, the first recorded McCulloch, Thomas MacCulagh had a coat of arms featuring a squirrel. (One is left to ponder the implications for the theory that MacCulloch derives from “son of the boar”).
According to the Clan Campbell Society of North America, the only authority on the use of a tartan is the clan chief. Therein lies the rub. Since Clan McCulloch has no current chief, there is no clear authority on what tartan a McCulloch should wear if they are so inclined to do so. Vendors will certainly sell you a tartan that is described as McCulloch. However, it is likely a personal, modern design. If you would like to register your own tartan, you may be able to register a new design with the Scottish Register of Tartans.