Robert Burton was an attorney who lived near Grayson County, VA in 1792 - actually across the state line in what was then Wilkes Co., NC but is now Allegheny or Ashe County. Vincent Jones (who married Alexander Trent and Jane Burton) was a JP as well as a Baptist minister who also lived in NC in the same modern counties and had been a leader there since the late 1770s. Being a JP, one suspects there might have been a record, but it would likely be in NC, not VA. Robert Burton later moved to the Hawkins Co., TN area. Interestingly there is a Robert Burton, son of William Burton of Bedford Co., VA who is a student at William and Mary College in the 1770s where he likely received a law degree (all I can say for sure is that he was inducted into the Masonic Order). Some of this I got by e-mail from Charles Osborne, the well-known Osborne family researcher, some from New River Notes and some off other internet sources.
The Robert B. Trent in Putnam had the nickname "Bert" which could be short for Robert or Burton. The information you provided agrees with what I got from a descendant of Bert's.
James Quinn - NJ -- PA