Fascinating that a few of the most famous horses of all time (Man o' War, Seabiscuit, Native Dancer) didn't accomplish this feat. I guess there's a lot more to horse racing (or at least there used to be) than just the Triple Crown races.
Man o' War's owner didn't run him in the Kentucky Derby. The "triple crown" didn't exist back then, and the Kentucky Derby wasn't considered as important as it is today. Man o' War's owner didn't like racing in Kentucky and kept him racing mainly in the east. Native Dancer was fouled twice in the Kentucky Derby and couldn't recover the lead. As for Seabiscuit, the lesson of his story would be to never share a birth year with Man o' War's son, War Admiral.
Why is it that race horses always have to have incredibly weird offbeat names? Who started that tradition? And why has it persisted for over a century? Don't rich people ever get tired of naming their horses things like... Tutenkhamen's Raspberry? Topaz Ballad? Loading Zone? Lingerie Stain? Rusty Alternator? Precocious Ottoman? Cheezwhiz? ... I mean... what the hell? Are they trying to give the horses low self esteem so they feel they need to run faster to prove themselves?
I'd name my horse Frank or Bob just so the call down the back stretch would sound really silly. And then, of course, there's always Hoof-Hearted. (one of the funniest calls I've ever heard)
Some people name their horses after a famous sire - War Admiral was the son of Man o' War. I had a co-worker whose horse was a descendant of Bold Ruler and they named it something that included Bold in the name. Horses often have a "birth name" but have to change it for racing - Big Red became Secretariat. Mostly it's because of the Jockey Club rules. http://social.derbyexperiences.com/bid/202895/the-rules-of-naming-a-race-horse
Only won one race - sadly it passed away at 4, sometime last year I think.