Not sure if this answers your question, but in the case of Duncans ...
Duncans were later known as "Septs" to the more dominant clans The Duncan – Donnachaidh – Robertson, Scenario by John Duncan of Sketraw. (Clan vs Sept) Duncan names were included by a happy accident that they lived within control of the dominant family, in specific areas, rising to power as the clan system formed. Septs pledged fealty to their "lords".
I suspect this is also true of other clans depending on the location and time period of who or which was the "stronger" clan in a particular area. Many intermarriages, also contributed to the multiple clan perception. (see Wikipedia link above re "septs")
Regards,