I named mine Hera. I named Link Zeus, so they went together. That was my first game of Twilight Princess. After that I kept Epona as Epona and Link as Link.
I like to stay true to the game so I named mine Epona. But I know someone else who didn't want to use the same name as I did and came up with Saria. I thought it was very creative especially since TP likes to look back on OoT alot.
Well, since I'm a big fan of Ocarina of Time, I decided to keep Epona's name as her own. Of course, I've usually made Link keep his name as well.
When I made my friend play Twilight Princess, he decided to give Epona a, well, not suitable name. Some friends I know have also named Epona after some horses they actually own, in addition to pets.