When working on the Carter emancipation documents, I came across this information. I will do same for other surnames. Hope it's useful I don't have a 1796 addendum to Robert Carter's original 1791 list, and someone who has access to that might be able to add/correct.

Dickson/Dixon

There were two Dickson families emancipated among the Robert Carter slaves. Original emancipated individuals and some offspring remained in Virginia, in Westmoreland County. The name shifted back and forth from Dickson to Dixon.

(Carter list, means handwritten 1791 list; Barden-Carter list means the typed list compiled by John Barden)Barden's list gives surname, first name, birth year, plantation assignment, year of emancipation. It's alphabetical. Carter's original handwritten list has (with a few rare exceptions) slave name, mother (less often father) or wife, age, plantation assignment. So, working up the families from the Barden list means finding the surnamed individuals on the handwritten list, checking birth years, plantation assignments, mother/wife link,then double checking.

Family 1: Solomon and Sukey Dickson
Solomon, 1743, Nomony Hall, emancipated 1793 (Barden-Carter); not on original Carter list, perhaps addendum
WIFE: Sukey (Suckey) Dickson, 1760, Nomony Hall, emancipated 1793 (Barden-Carter list); Suckey wife of miller Solomon, 31, Nomony Hall. (Carter list)
SON:Billy Dickson, b. 1778, Nomony Hall, emancipated 1799 (Barden-Carter list); Billy, son of Suckey, 13, Nomony Hall (Carter list).
SON:Moses Dickson, b. 1783, Nomony Hall, emancipated 1804 (Barden-Carter); Moses son of Sukey, 8, Nomony Hall (Carter list)
DAU:Nutty Dickson, b. 1785, Nomony Hall, 1803 (Barden-Carter list); Nutty daughter Suckey, 6, Nomony Hall (Carter list)
SON: Elijah Dickson, b. 1786, Nomony Hall, emancipated 1807 (Barden-Carter list); Elijah son of Sukey, 5, Nomony Hall (Carter list)
SON: Solomon Dickson, b. 1788, Nomony Hall, emancipated 1809 (Barden-Carter list); Solomon son Sukey, 3, Nomony Hall (Carter list)
DAU:Jemima Dickson, b. 1790, Nomony Hall, emancipated 1808 (Barden-Carter list); Jemminey, daughter Suckey, 1, Nomony Hall (Carter list)

Perhaps Solomon child by earlier wife, as not name-linked to Sukey:
DAU: Polly, daughter Miller Solomon, 17, Taurus (Carter list); unclear what surname she is under on the Barden-Carter list, as the only fit is Polly Wells, 1774, Taurus, emancipated 1792.

1850 census
1. Solomon Dixon, Cople Parish, Westmoreland, VA, 30, M, farmer, VA, married to Emily, 30, B, dau Susan, 10, M; James 4, B Frances 2, M Solomon 3, M; Cephus, M, 7 months, John Thompson 22, B, laborer. M432-980, p 286

Next household Billy Dixon, 70, Judy, 70, Laurenda Harrison, 13, Nelson Jones, 10. This appears to be Billy Dickson, b. 1778, Nomony Hall, emancipated 1799 (Barden-Carter list); Billy, son of Suckey, 13, Nomony Hall (Carter list). The only Judith on the Carter list within the right age range is “Judith from Old Ordinary,” 14, Aquarius; which seems to match Judith Banks, b. 1777, Aquarius, emancipated 1795 (Barden-Carter list), particularly given the absence of other Banks on the list.

Dickson Family 2
William Dickson, b. 1752, Nomony Hall, emancipated 1792 (Carter-Barden list); Gloster Will, 39, Nomony Hall (Carter list)
WIFE: Prue Dickson, 1762, Nomony Hall, emancipated 1793 (Carter-Barden); Prue, wife of Gloster Will, 29, Nomony Hall (Carter list)
No children are linked to either, on the 1791 Carter list, and all of the Dickson children on the Barden list are accounted for as Solomon and Sukey offspring. One possible offspring of William with a first wife is "Sarah, dau Gloster Billy," but seems likely "Gloster Will," and "Gloster Billy" were two different individuals.

1810 Census, Westmoreland County, VA shows William Dickson Sr, and William Dickson Jr. households (Roll 71, page 244, image 465.00). Wm Sr. had 1 FPOC, no slaves. Wm Jr. has 5 FPOC, no slaves.

1820, 1830 censuses for Westmoreland show William Dixon, FPOC and a Nancy Dixon, another household. In 1830, William Dixon, 55-100, six in household.