A couple of real examples:
For the absent-minded race caller: Bucket of Vyno
For the race caller in the cramped, stuffy studio: Hoof Hearted
My fantasy horse:
Tripod
out of Wilhold by Elmer’s 
Some of my favorites (all real racehorses):
**Thisdudsforyou
Arewehavingfunyet
El Hombre Rapido
Chingoso*
Hoovergetthekeys
Kitty on the Track
Nonsuch Bay
You (she’s a big star right now–makes for hilarious headlines: “Yoe made it to the Winner’s Circle!”)
Behave Yourself
***This is Spanish for “fucker.” The horse had already won a few races, including placing in a stakes race, before the Jockey Club caught on and the name had to be changed.
There was also, IIRC, a horse running in Australia whose name was a term for female anatomy, spelled backwards (I don’t remember if it was a technical term or slang). She, too, had to have her name changed once it was caught.
Rooting King 
I always thought Commendable, the 17-1 winner of the 2000 Belmont, had a real champion’s name. In fact, on my principle of taking the D. Wayne Lukas horse in the Belmont (a principle which has proven wrong in the last couple of years), I bet $50 on Commendable, and won $850 for my prescience. Dig it.
Real Aussie horses:
Chicken Lips
Tangfu (Typical Air New Guinea F*** Up)
Merkin (look it up)
Bet Twice
Eighteenlettersmax
Hatetosayitoldyaso
Aheadbytwofurlongs
Sofa King Fast
Avluv?
Anyway, favorite actual horse names so far have been:
Spank the Money ((Red Mile - Everyone thought it was a typo.))
and
BJ Copperbottom ((My mom’s horse.))
Cabbage - is ahead!
And bringing up the rear is Beetlebum!!!
Harass
Pre-race announcement: Harass has been scratched; scratch Harass.
I seem to recall a horse named Bodacious Tatas.
I tried Googling for it, but apart from the predictable results, all I got were sites devoted to some WIPO domain-name dispute case.
Gallopoli
Toshoindathird
PeterShaffer’sEquus
Not a registered TB name, but a friend used to have a horse she showed under the name “Buck Naked.” See, the annoucer names the horse/rider combination when they enter the ring to jump: “This is [friend’s name], riding Buck Naked.” Really draws a crowd, har har.
Well he wasn’t a racehorse, just my horse when I was little.
“Ringo” (I named him myself)
The Wonder Pony’s[sup]TM[/sup] registered name is Whata Sweet Talker. Screams Quarter Horse. But his real name is Bob. His mama’s name was Benlou Glo Squirt (ick). Canopener is the sire of my friend’s horse. I love the name Count Fleet (1943 Kentucky Derby winner). There’s a gazillion funny/odd/sick/stupid/“risque” horse names, especially ones that are really typey of a breed or discipline. The horse boards I participate in usually have at least one thread going about names.
peedin do you post on chonofhorse.infopop.net? More English-discipline oriented but some really good conversations. I think of it as the SDMB of horses.
BTW, Hello Again is my horse’s show name. You know how you always see the same people at every show…
My Anglo-Arab’s registered name is Pep N Glo. I just call her Pepper.
Why do I always hit submit too soon? I have also owned Buckana Leo (QH) and Cactus C Bars (Appaloosa). Buckana and Casey for short.
Arkle and Foinavon were both extremely famous racehorses, for completely different reasons. Foinaven was a plodder who won the flukiest Grand National Steeplechase ever in 1967. Arkle was a great flat-racer (I think also in the 60s, correct me if I’m wrong). A sharper contrast could not be made between two race-winners.
However how many race-goers know that Foinaven and Arkle are actually two neighbouring mountains in western Sutherland, in the most remote and desolate part of the Scottish Highlands? You think you know what the Highlands look like, but if you saw this area you would not think that it was even on the Earth, let alone the same island as London, Sandown and Epsom.