The moon is dying.
A dog howled, and she answered.
[A dogs howls, and now she answers?]
After years of barking
the moon turned and bent her neck,
stooping down to kiss the mutt.
[i think shifting the tense here to present allows you to work your moon as ongoing myth angle other wise it falls flat and you have an unflattering murkiness w/ the next part]
Or is it,
is it that she one day saw him,
filthy with matted hair,
standing outside the house with the porch light on,
[i think this should to be changed to: is is that she one day saw him,/ with the porch light one,/ filthy with mattered hair, standing outside the house,/]
[i feel that you’ve misattributed the porch light to his being rather than her seeing, i think that the above suggestion corrects this clumsiness and reinforces your poeticism w/ minimal change to your rhythms]
and thought him handsome.
[i think that if you keep this tense you have a story, in contrast to myth but not in opposition, whatever [harrr!] you’re showing another side to this myth story]
Whatever the case,
the moon is dying.
Every month her eye bruises,
the moon is a chew toy.
The dog won’t stop gnawing
on the flesh, the rocks will disintegrate
into moondust, and I’ll be there, a speck
[perhaps? “to dust, and there i’ll be a speck”]
holding up the moon while she bleeds out under the dark sky.
[and like here in this third part you’ve brought your story and mythic together and there’s a strong sense of the narrator struggling understand and come to a sense of terms w/ their actions and role]