White People's Names

I've been looking at my family tree recently, a part of which is of the Cherokee line.
These ancestors of mine were obviously trying to fit in with the white people who were now everywhere, and you could tell they were trying to give their kids white people's names.
"What are white people called?"
"I don't know, they all have names like William or Willie or Jesse or something."
So my great great grandfather, whose name was Jesse, named his kids William(who died young), a girl named Jessie, then William, next was Willie, Edwin/Edward and Sally(my great grandmother).
A couple of generations before that they had an even harder time. It looks like they only found White names from books. These are the names of my great great great great grandfather and his brothers and sisters:
Henry, Mary, Rattlinggourd, Pink (Pinkney), Martin, Mark Anthony, Hardin, Washington,
Jefferson, Susan & Elizabeth.
A different part of my family tree was made up of pilgrims who came to America very early. Many of them married natives, one of whom was very religious-a "praying Indian", and they named their son Ami Ruhami. This is something from the Bible, which I guess is a different way of finding White People's names.
I think they would've been better off with my Random Name Generator, don't you?