Hi! I actually don't know for certain if the the N stands for Noel. All I knew until very recently was the name and the children, again from a court document.
I was contacted by another Davenport descendent who also thought this was Jonathan Noel Davenport and provided some information from oral histories of a grandmother and great-aunt who grew up in Washington Co. VA. They said this Jonathan was married to Charity Whitaker and was son of Jonathan Davenport and Patsy Cothin. This Jonathan had a brother, Edwin , which fits the Edwin Davenport who adopted the orphans.
Do you have any information on John Noel buried in Wash Co.? Also you mentioned a Claiborne - how is he tied to John?