This post follows on Fun with the McFunns where I tried to work out where the given name for a girl Hamilton came from.
I had a message from a lady in Canada descended from Hamilton Lesley mother of Hamilton McFunn. She said it was her understanding that Hamiltonia Lesley b Cambuslang in 1757 was named after a Covenanters' victory at the "tiny village" of Hamilton.
I asked my husband about a famous Covenanters' victory and he immediately said the Battle of Drumclog in 1679. Wikipedia confirmed this. Drumclog is a tiny village but not terribly near Hamilton so that didn't make sense. However Wikipedia says the commander of the Covenanters forces at Drumclog was Robert Hamilton. Could he be the source of all these girls called Hamilton? Why not call the sons Hamilton? There did seem to be a tradition of calling girls by surnames.
A search of Old Parish Records on scotlandspeople revealed 848 females named Hamilton but all were from 1730 - 1854. Seems a bit too long after the event. However, few records exist before 1730. The jury is out.