Although Tartans were not always representative of one’s clan (rather, they were more commonly representative of region and personal taste), around the start of the 19th century, more regulation began as a way to distinguish weaves commonly worn by different Scottish clans.
Naming and registration of clan tartans began on April 8th, 1815, and most clans were keen to provide their own designs. Over time, they also developed alternate designs, but maintained an official clan tartan.
The tartan which Montgomery Scott is seen wearing in episode 3x22- “The Savage Curtain” is not the official clan Scott tartan, but rather, a variation featuring a black and white weave, which he was given the blessing of wearing by members of the clan, despite being of Irish heritage.
Even just a few years before his passing, actor James Doohan could be seen proudly wearing the Scott tartan on the red carpet, a symbol of his most well-loved character and his adopted heritage!