I have always loved naming animals, especially horses. Luckily my best friend's family breeds a number of horses and I've had a couple of opportunities to name some of their horses.
My first horse, Red, came with his very unoriginal name. Since he was 14 already, I decided to keep his paddock name. We looked up his racing records and found out his racing name was Tin Solider (and that he also had not won any races). Again, I wasn't impressed. If I was going to compete him, I wanted him to have a name that meant something to me. I thought about it for ages. I considered putting Red somewhere in name... Red Sunrise, Red Sensation, Red Robin. The Red Robin got me thinking and I remembered Christopher Robin from the Winnie the Pooh books. I used to love the books and movies as a child and my it also was special because my mum used to always call my cousin (with whom I grew up with) Christopher Robin (his name was Christopher) and used to quote "Christopher Robin is saying his prayers" to Chris often. And so Red's competition name was Christopher Robin.

When I got Jack, I also kept his paddock name. It suited him and I didn't think it needed to be changed. His racing name had been "Jack's Back" which I thought was pretty lame. Again, I thought about it long and hard. Jack is impressive to look at and commands attention. I wanted a strong name. Sometimes I looked at him and thought he looked like a battle horse, and he has a couple of scars on his leg that made me think of battle scars. So I started playing around with names with 'Battle' in it. I came up with 'Battle Cry' which suited him amazingly. He is very vocal and it fit well. I haven't registered him with the New Zealand Equestrian Federation yet and it may be that that name is already taken, if that is so I am going to put my second and third choices down as War Cry and Battle Master.
My cats also have names that mean something to me. Chucky, our first cat, came with his name. He was ginger and was named after 'Chucky' from the rugrats.
Muffin was named by my brother (i'm not sure why). It has been my experience that if you name cats after food, they get fat. It might night be scientific, but its what I have seen. Muffin is fat, and so was my cousin's cat Donut. My friends cat, Chrunchie, was also a fat cat.
Next, Ellie came into our lives. Her real name is Al Queda (if that offends you in any way I am sorry). She used to terrorise the other two cats and also us, when she was a kitten. The name was given to her as a joke and we call her Ellie at home.
I got Forrest last year, and had named her before I thought I was going to get her. She looked like a cat from the Forrest, and I also love Forest Gump. It really suits her, so it stuck.
How did your horses and pets get their names? I'd love to hear.