Yep, clan chiefs are definitely HSAs, under the Scottish Clans Project.
As a general rule, we use the names people used for themselves, rather than what we find more convenient. The one place where we've deviated from that is with nobles who don't really have last names, in which case we use the name of their house, or lacking that, a name given to that dynasty, etc. Some people are of the opinion that we should expand that practice to other groups, like these clans, where the last names are not passed down from father to son, but personally I feel that's going too far into applying our western naming conventions where they don't belong.
My 2 cents! :)