There are no strict rules on who has the right to wear a particular tartan. People normally wear only the tartan (if any) of their surname, or a “district tartan” connected with where they live or where their family come from.
Wearing a particular clan tartan indicates that the wearer bears an allegiance to the chief of that clan. A tartan which uses the name of a clan may only do so if the chief of that clan has given his approval to the particular design.
Tartans are now registered is with the Scottish Register of Tartans, the keeper of whom is also Keeper of the Records of Scotland. This superceded the Scottish Tartans Authority (which still exists) in 2009.