Okay, after careful observation of the good Reverend's illegal twitpic taken on the set of "Green Harvest", I see 21 tombstones, of which I can decipher 19 names. They are, by row, from left-to-right:
1. J. WHITE - In Our Hearts Forever and Always
2. K. PEREZ
3. J. GREEN - Her Gentle Spirit Will Shine on Us
4. In Loving Memory - WHITE - Beloved Brother
5. D. NELSON - In Our Hearts Forever In Our Minds Forever
6. B. EDWARDS - A Dear Mother and [???]
7. R. SMITH
8. S. MILLER
9. J. SCOTT - Forever in Our Hearts
10. J. LYNN
11. G. ALLEN
12. J. JACKSON
13. R. NGUYEN
14. D. JONES
15. A. RIVERA
16. N?. WILSON
17. In Loving Memory - BROWN
18. L. BROWN - [???] [???] [Uncle?] Friend
19. In Loving Memory - JONES
20. [??? Possibly another JONES]
21. In Loving Memory - [???]
Two (maybe three) Jones, two Browns, and two Whites suggests that this is a small community of close families, and we may have characters with these names.
There are at least two women (Green and Edwards) and one (White), possibly two men (L. Brown), but due to the lack of first names it's impossible to tell genders outside those with descriptions. The two Browns next to each other might be a married couple, but there are no other signs of joint burial plots as is common around here.
D. Jones might be a reference to actor Doug Jones. Other than that, though, I don't recognize any of the names amongst Discovery's cast and crew.
The names are very monocultural (other than Nguyen, Rivera, and Perez), but even moreso they're just plain common. We have both Smith and Jones (several of them), as well as Brown, Miller, and Wilson. Five of the top 10 last names in the United States. Most of these names are probably not written by a writer with a thoughtful history behind them. Just random names, I would guess, thought up by someone in production design.
Except for Rivera (#61), Nguyen (#229), and Lynn (#862!), all the names (13 out of 16) are in the top 50 of the US Census Bureau popularity list.