You can't. Ever. The only horse in the game you can own that has a name is Shadowmere, which you'll receive after progressing through the Dark Brotherhood questline.

You forgot the horse Frost.

You can't name your horse really unless you get the special ones later on in the game like shadow-mere. and yes its kind of stupid in my opinion. But there is mods on the computer in which you can do that :) hope this helps

Its already named for you. I mean that its named by your Skyrim Traveller (which is you) and thats how! Also I found a glitch if you sprint on your horse and get off with the horse still sprinting you should get infinate sprint aswell! But just dont press the start menu or anything! ; )

And you cant really rename it. Sorry.

Yeah... about that.... you can't rename it..... yeah.... so..... um... yeah

You chould make a mod to name the horse.But you need the pc vershon and have no life