Whatever the case, I would say it's fair to name a realm after an animal if that animal has some kind of RPed cultural significance. Seems a plausible enough thing to do.
A better practice, of course, would be to name realms off of people groups; either of the nobles or of the commoners. As Dwilight does have a formal geography, and is developing an ethnography, this is plausible.
But, honestly, it doesn't matter that much. Realm names are historically dubious. In a few years, Solaria and Kabrinskia will just be realm names, like any other.
Also, there are several precedents:
Kronos' Burg, Atamara
Soliferum, FEI
Raivan Empire, Dwilight
Valhus, Beluaterra
Luz de Bia, Beluaterra
Lemundia, Beluaterra
Capashinia, Atamara
And those are just the ones I am sure about. There may be more.
Naming the realm after yourself is probably one of BM's most common naming conventions, after "Location Name" and "Succession Names."