David Beckham?
How do you need a famous person's permission, when we've had a line-up of George Washington, Dylan Thomas, Alexander Pope, Flintoff, Zukhov, Putin, Titus Andronicus, Galileo, Yeats - in fact, any amount of famous painters, poets, writers, philosopers, politicians, emperors and sportsmen? There are no doubt heirs and assigns of some of these living today, and it seems that anyone can name a library or museum after them if they wish, without requesting the permission of any surviving families.
You probably can't use a trade name if that's copyrighted, such as Spiderman, but there'd be nothing to stop you calling a horse Michael Jackson, because there are probably thousands of males with that pretty common name. We've got BARACK these days, and I doubt that the Prez was asked, because no doubt there are a few more Baracks in the world.
Surely, unless the person has copyrighted the use of their name, you're free to use anyone's? It might be that people whose name is used by them to promote a line of products, such as Victoria Beckham, might have copyrighted their name and therefore it could not be used in a commercial sense, but I'm not sure that a racehorse would be considered a business.