"Inubashiri" literally means "dog running". It can also refer to the dirt path outside of castle ramparts used for patrols.
"Momiji" is one of several Japanese names for maple trees. It can mean "Maple".
This is official to an extent as she is depicted with detached sleeves and wolf ears in the first chapter of Oriental Sacred Place (see right).
Aya's spell card comments in Double Spoiler, however, contradict this personality somewhat, as Aya comments that she and Momiji tend to easily get into fights whenever they meet. Aya also comments that Momiji looks down upon the Crow Tengu. The remarks note that she still serves the Great Tengu faithfully. It should also be noted that fellow Crow Tengu Hatate's spell card comments suggest that this might be a more personal feud between Momiji and Aya. Hatate herself seems to hold Momiji in high regard.
Her profile says she plays Dai Shōgi, a game similar to chess, with the Kappa. Because of that, some fans think that she personally knows Nitori while taking a break from her job.
Momiji's wolf-like appearance may be a reference to the Tiangou, a Chinese version of a tengu that are described to be more dog-like.
Momiji makes two appearances in Symposium of Post-mysticism that look similar to her appearance in Oriental Sacred Place, however, she doesn't appear to have wolf-like ears. In addition, Kanako's Newspaper article includes two White Wolf Tengu, one of which is Momiji. The unidentified White Wolf Tengu appears to have ears and longer hair whereas Momiji in both appearances in Symposium of Post-mysticism does not have ears. It is unknown as to whether or not this is an error or Momiji truly just does not have wolf ears, unlike her appearance in oriental Sacred Place.