I agree with the ohers - quite common to give surnames as middle names to girls. I have several in the families I am researching. I also have Scottish Lamonts in one branch.
The first place to look for any connections is family - grandparents and great grandparents etc, but the surname as middle name could have come from elsewhere, and you may never find the connection.
I have a record of a document where the Scottish father was talking about his children and explaining how many of them were given their middle names. He also requested that these middle names be passed down the generations. One that sticks in my mind is that one of his childen was given, as a middle name, the surname of someone who was "kind to his wife". Another family gave their daughter the surname of their employer as middle name. It is generally done to "honour" someone who the family hold in high regard.
One of my favourites is the family (not Scottish) who gave each of their ten children the same middle name - in this example I know it was the mother's maiden name.

There will be many other similar stories.
