I like "Olly by Golly" as a show name, out of the possibilities mentioned here. It's cute and endearing, and shows some personality. Naming a horse after an inanimate object (such as a bounce house) has always seemed weird to me. And if you use "Bounce House," all these variations on the spelling of the words just seem like silly stretches to make it more "European" or something. Remember the "KISS Rule"? For those not familiar, it means, "keep it simple, stupid". As for me, if given the opportunity to name a horse I like to select something that has personal meaning to me. Something coming from the name of my favorite artist, painting, song, poem, or a favorite place that I may have gone on vacation, or an image from my childhood, such as the name of the street I grew up on, etc. Whatever you name him, I wish you the best of luck in the ring!!!
As a teenager, I was waiting to go into the ring at a show and I remember this assistant trainer from another barn prattling on about "twilight sentinels" in vehicles and I kept thinking, "wow, this chick is weird." For some reason, I will always remember that.