I have a number of Scottish ancestors who all had unusual middle names, and it seems that there was a tradition of naming children after family members and close friends but including the whole name!
For example, my g-grandmother: Isabella Gerrard Meldrum Eden was named after a womand called Isabella Meldrum, nee Gerrard who had been her mother's neighbour when she was a child. I have a lot of people just like this so it's possible that your family used the same method!
I have the surname of Dunthorne on my family tree. I wonder if that is what they meant?
My husband's ancestors quite often had a surname as their middle name. One was named Henry Richardson Norris another was called Grace Witham Norris. I think the surname came from a friend of the family or another family member's surname. It's often someone they wish to honour so they add it as a middle name for a newborn child.