Irisia has a few from her past. Dreadsong, Deathbringer, Death Dragon, Life Devourer, Hydaelyn's Terror, Reaper of Life, these being her ones from the people of Rabanastre, mostly bandits and poacher. The Rava knowing her as the Dark Guardian and this is one she does not mind. (Cont. in Comments)
There is one other name she has been given and it is the one she detests the most, which is 'Kin Slayer'. A name given to her by her mad uncle in their final encounter. The name itself is traumatic for her, mostly because it is a truth she hates. In defending the star, she has laid low her own kind.
As for now, Irisia goes by just her name, leaving most of those names in the past, minus one of them. Karrina on the other hand does not have many nicknames, just those of the village. Those being Lightdancer, Holy Dragon of the Mountain, and Life Mother.