If I'm not too late, I'd like to try my hand at this too.
Articuno: Halla, a Finnish word a weather phenomenon where the temperature drops below zero during the growth season. It's usually very beautiful when the whole world seems frozen over and all the plants and trees turn silver. I think Articuno's presence might have a similar effect if it were real lol.
Or
Frosti, a Björk song, pretty self-explanatory but still very beautiful and fitting.
Zapdos: Volta, a Björk album this time, and again pretty obvious, but ever so cool and fitting.
Moltres: Helia, IIRC a daughter of the Greek sun god Helios.
Or
Aska, Umm not so sure about this one's origins. I've just always loved the name Aska and ever since playing Tales of Symphonia I've thought Moltres should be named Aska. There's this Spirit of Light named Aska who is the spitting image of Moltres. Light can also be taken to mean the sun which obviously means infernal fire and is very fitting for Moltres.
The reasoning behind my nicknames for Pokemon and naming things general is pretty simple. I want something really cool, beautiful and different, but something that still actually sounds and feels like a name, is easy to pronounce in most languages and fits its bearer's personality and characteristics.
My favourite combo of these is Halla, Volta and Aska which also compliment each other remarkably well. Oh my, I might actually have to NN my next competitive birds Halla, Volta and Aska.