That's my theory as well, but I just noticed that the moon necklace also has a little star beside the moon, Stella means star so who knows, maybe Luna is a pseudonym Noctis is using to talk about Stella, or perhaps her name changed from Stella Nox Fleuret to Stella Luna Fleuret or something like that.
I thought Lucis was the name of the whole kingdom, maybe Insomnia is just the name of the city/capital. I mean it is part of Noctis' name (Noctis Lucis Caelum) and his father is Regis Lucis Caelum.
You might be right, but I was always under the notion that all the cities are far apart. I think Lucis/Insomnia is standalone.
'The Royal Capital' says otherwise, though. Hmm...