Unfortunately, I have very limited information.
I spoke to my dad's oldest cousin, whose in her 80's, and she was told this by her father.
For some reason, the family line was not really discussed, but her father gave her this info when she was a child.
I tried to do some research, and found a list of those who had been Knighted.
To be honest, i'm not sure if the original surname was only Pilkington or Williams. I'm also trying to find out whether those knighted had surnames added, which would explain the double barrel surname, but not sure whether this is true or not.?
Apparently, my one of my grandfather's brother's went to England to try and find family. It seems that because Lord Molyneux never knew about the birth of his grandson, the inheritance, was bestowed upon the "next in line" male in the family. I don't think any friendships were made in this endeavour, so not sure what happened there.
I do also know that Pilkington was a 2nd name passed onto all male heirs, or if a female was the oldest, she would get the name, for example, other family members of my dad: Sharon (the eldest), and her brother Craig both have Pilkington as their 2nd names and their surname was Williams, but the youngest daughter does not have the Pilkington.
I know that it's very confusing, but my grandfather was a Pilkington-Williams, not a Williams, and because there are so few of us, I'd love to find out more about my dad's side of the family.