It’s not bad for a first sonnet, but since you asked for harsh criticism . . .
My main note is that this piece doesn’t say anything new. People die, and the living forget about them. It has the rhyme scheme and meter of a Shakespearean sonnet but not much of a volta; the couplet is more of a summary.
Line notes:
Of Names Forgotten
The postpositive adjective is somewhat archaic, though not out of place in this subject matter.
Where all the people lie at rest in stone,
“At rest” isn’t doing much here.
Entombed with others lost in dark embrace.
- “Entombed” is implied by “lie at rest in stone.”
- “In dark embrace” is missing an article.
- The first two lines are a sentence fragment. There’s a time and a place for fragments; I don’t think this is it.
Of fire and flames or age and rot, their bones
Both “fire” and “flames”?
Still lie inside this deeply hallowed place.
“Lie” is repeated; unlike the best sonnets, this poem is in no hurry to get where it’s going. “Deeply hallowed” strikes me as received language, and “place” is nebbishy for how prominent it is as the rhyme that closes the quatrain.
In ordered rows of whitened stone inhumed
More archaic syntax with the postpositive “inhumed.”
Are hopes and visions cursed to never pass.
Close to “hopes and dreams.”
So many graves that sit abandoned—doomed,
Em-dashing “doomed” like that makes me feel as though it’s there only to close out the rhyme.
So few with flowers or well cared-for grass.
First metrical substitution. Fine, but note that the rest of the poem being so iambic draws attention to it.
When placed like this they lose their meaning too,
No notes.
Each stone the same as every other is.
More inversion.
Forgotten is what rests beneath the yews,
The rhymes to this point have been perfect, so “too” / “yews” feels a little sloppy to me. Fronting “forgotten” is more inversion, but this one works for me.
A corpse with friends, a life, a dreams and sins.
“Is” / “sins” feels more than a little sloppy.
The many gravestones lost by time and men
Will fade in memory, again and again.
Second metrical substitution. This one is two anapests for an iamb, which most form poets do not countenance. (Maybe you want the alternative three-syllable pronunciation of “memory” and an anapest for an iamb; rather more acceptable.)
Hope this is useful.