That is the 1780 Tax List for Dobbs, Lenoir and Greene Co NC.
Scroll down to District 8, Greene Co, NC.That tax district covered the area West of the Great Contentnea Creek, in Northeastern Greene Co, adjacent to the Wayne Co line.
You will find Thomas "Aldrich" on line 8-36.
On line 8-6 you will find William Faircloth.
You will also find a bunch of Smiths, who are 'married in' with the Aldridges from Northampton Co, NC in the 1750s. I'll go into that later if you wish.
If you google Dobbs County NC Grantor-Grantee Deed Index you will find there a Druery Aldridge who was probably there in 1760s.I think he was the father of your Thomas.
Druery Aldridge and his sister, Mary, were children of DREW ALDRIDGE (m) Mary Smith.Drewry and his sister Mary are named as grandchildren in the will of Richard Smith, written 1751 (P)1756 Northampton Co, NC.Mary Smith Aldridge was that Richard Smith's daughter.
Now, backing up further in time, we find John Aldridge's will in Bath Precinct NC, undated but Proven at the Bath Court on thefirst Tuesday in April 1702.RICHARD SMITH witnessed the will.
The line of Richard Smith comes out of Surry Co VA, and I'll betcha your Aldridges do too.,
I've been digging in the Smith rabbit hole for quite some time now....sorry to pull you in after me.
The best source for good documentation in Surry Co VA, imo, is the Surry County VA Tithables List.It covers males over 16 from 1668 through 1703.It's hard to get but I have it filed.I'll look for Aldridges and post again....if you wish.