In the sentence, "And now Miss Emily had gone to join the representatives of those august names where they lay in the cedar-bemused cemetery among the ranked and anonymous graves of Union and Confederate soldiers who fell at the battle of Jefferson," the word "august" can best be described to mean:.

The word "august" is used to refer to mean "distinguished or respected".

Explanation:

A Rose family is a short story penned by William Faulkner in 1930.

In the story, the author used the phrase "august name", in the second paragraph while writing about Miss Emily and commenting on her death and funeral.

Th author, Faulkner has used the word "august" which means "distinguished" or "respected". Faulkner used this word referring to the names of those families who were buried in the same cemetery as Emily.

The phrase "august names" is used for prestigious families who owned plantations and those individuals who were ranked Confederate soldiers.

So, the correct answer is "distinguished and respected".