Trajan is a silver-haired bat (Lasionycteris noctivagans).
If you've read 'underneath it all', you know how he came into the picture. He lived in the attic of the Adil home at first, and entered/exited through a ventilation grate under the eaves. Naturally he's nocturnal, but if something's really up...he can jostle himself awake long enough to get involved. When Theresa moved away from home, he came with her, finding a way into the upper crawlspace of her apartment building.
Trajan is long on philosophy and generally short on words. Usually the two traits don't go together. He likes cryptic phrases and won't always give a straight answer, and will get annoyed if folks don't think for themselves, especially Tisiphone/Theresa. He can be a little pompous and formal. He also prefers folks to think of him as intimidating, rather than 'cute'. He takes his job as a guardian very seriously--probably a little too seriously, and tends to involve himself even when it's got nothing to do with him. He tends to be a little nosy about Theresa's life, and has opinions on everything, especially Rob. Theresa once accused Trajan of being jealous, after which she didn't see the bat for three days. Now she knows how to get rid of him! Rob's only seen Trajan once, by accident, and didn't think anything of it. Theresa, once she got used to Trajan and the whole idea of who he is/she is, liked to hum the 'Batman' theme at him and quote from the original Batman series, which he still finds hideously annoying.
Theresa looks for ways to purposely unsettle the bat, and despite his constant protests, he really doesn't seem to mind much. He threatens to leave, often, but obviously he's still around. Would-be senshi and loudly complaining guardian play off each other's words constantly and refuse to admit that they've gotten used to each other and look forward to each other's company.
Silver-haired bats generally eat insects, but this one in particular has a thing for jujubes, just like Theresa does. She manages to 'accidentally' spill a few on the windowsills now and then, and pretends to know nothing about it. When they vanish, Trajan pretends it had nothing to do with him, and that works just fine for both. There's a curious-looking piece of art hanging from the ceiling in Theresa's extra room, made of colorful wooden dowels that are sturdy and stable enough to hold a hanging bat for when it gets too cold outside.
Trajan doesn't talk much about the past or his true origins beyond how it directly effects Theresa's role as Tisiphone. He can change the subject at about mach 5 and then vociferously proclaim he's NOT evasive.
the myth and history:
Trajan was a Roman soldier who worked his way up through the ranks and was adopted by the then-emperor, Nerva. Trajan was emperor from AD 98 to his death in AD 117. He was one of the most successful conquerers in Ancient Rome.
Bats are often connected (unfairly) with death, darkness, and destruction, and even vengeance. The Guiana Indians of South America told a legend about Boku-boku, the night owl, who married Bat's sister and often took her brothers at night to rob people's houses, frightening them with his strange cry. Once when the owl was hurt, the brothers went by themselves to rob the village homes. Without their brother-in-law there to frighten the villagers with his cry, their cries were not loud enough to scare the villagers. The village chief shot one of the bat-brothers with a blunt arrow and stunned him. His friends were able to revive him though and returned to the village the following night. This night they were not as fortunate, the bat was wounded again and didn't recover. Ever since then the bats have gone about sucking blood of men and their fowls, to avenge their brother.
Well, it's a myth.