Hello Ellen:
I did not find Conrad's father's name, but I did find two web sites from a genealogy forum that may have a little bit of information that could help. From both, it appears he was born in Germany and came to America as part of the Hessian unit imported by Britain in the Revolutionary War. He apparently deserted the British at Jamestown and joined the Americans. I tried a couple of different search sites but wasn't able to find much.
https://www.genealogy.com/forum/surnames/topics/butt/963
https://www.genealogy.com/forum/surnames/topics/bott/570
At Family Search, I found a Johann Conrad Both (the record is in German so Both could be Bott ??) christened March 4, 1751 in Mutterstadt, Bayern, Germany. This may have nothing to do with your Conrad; however, you may want to check whatever German records are available. The record did have mother's name and I think the father's name also. Since it is handwritten in German, I have no idea exactly all the information that was there.
I realize none of this really answers your question, but maybe it could give you a couple of trails to follow.
Good luck, Margaret