Some of the more unusual ones I've developed over the years:
Sanae: Diimo
This came out of an RPG battle system I was working on; it was inspired by the spellcard system, so naturally I used Touhou characters while testing it. Sanae's ult was a (literal) godbuff called Divine Mortal's Blessing.
Alice: Petrushka (Petra for short)
Ripped straight from a manga (Gunslinger Girl), which itself stole it directly from a Russian ballet, which, as I understand it, is a lot like Pinocchio.
Mokou: Volx
I was mad for a while that I didn't have a nickname for Mokou, so one day I sat down and straight up crafted one. I ended up melding Volcano with Phlox, the Greek root for "flame." A very firey name, indeed.
Yuuka: Yuudorable
Vitamin Rice has a series of doujins starring Noukarin (Nouka ("farmer") + Yuukarin), who is the polar opposite of the typical fanon Yuuka portrayal. One of the splash images in the first book ("Daisuki Noukarin") was just so amazingly adorable, it demanded a new word to describe just how adorable it was. To date, only the flower master herself has proven worthy of the description.
I'm also fond of several common Japanese nicknames, such as Teruyo (born out of an alternate reading for the kanji in Kaguya's name) and Nezumin (Nezumi ("mouse") + Nazrin)
