My names just constantly change for my horses, and just depend on how I'm feeling with them. It is very much something that will just come about, rather than something you plan. I'll share mine that I can remember; they are quite ridiculous as a rule.
MM MAGS SUPERSTAR (POAC) aka "Moe". I call him Mooch, Smooches, etc. while my father calls him the names of terrorist leaders and the like; Mosama Bin Laden, Momar Gadafi, etc.
Sadie (Grade Paint, so techniquely a pinto,) she gets called Shady-Lady (we had a dog named Sadie, too, and I wanted to change her name to Lady, but that is as close as it got), Spayedy, and Slim-Shady (by my father mostly, but it caught on.)
Gypsy (Grade Morgan,) has been called Phil Shiffley as of late, off of some commercial and it stuck in my head. She is pastured with our weanling, Takala, so instead of saying both names I call them "Takipsy."
CMC Simitars Rose Red (ABCR) aka "Scarlet" was probably one of the harder to come up with a nickname for. Scar seemed slightly frightening, so I called her Car instead. Then it evolved to Carletto, Stilletto, Letto-bomb, Curletto. We still call her Letto and Letto-bomb constantly.
Tenakee, (ABCR) whose barn name is also Tenakee. Right off the bat we started calling her Tenny, then to keep with our Curly-horse shoe-names I started calling her Tenny-Shoe. So she gets anything from Neenerkee to Tenny-shooper-pooper, as well as Neener, Neen, and just "the Old Mare" even though Gypsy is our oldest.
Tenakee's 2013 filly, whom I named Takala, has plenty more names. I started calling her Lila, then it went to about a million different names; Tickley, Tackley, Tasquala, Tack-o-leelee-baby, Borse (baby-horse), Tequila, Ta-keel-a Mockingbird, etc. My dad, however, just calls her Lumpy.
Then we have our team, QH-Haflinger half siblings. Chester and Abby. I started calling Chester "Cheddar," and Abby took a while to think of, but I oh-so-creatively called her "Shabby". Once Abby's true personality came out, we started calling her "Crabby." But I will call her Shablicious to counter it every once in a while.
Some day it will come to you, and you will never call your horse by his name ever again! The longer we have a horse, the less we call them by their name. I listed the horses in order that we got them, so Chester and Abby yet to have anything too fabulous.