For ten years I've freelanced under a my web development and consulting business — SnapTortoise. The name was actually a recommendation from a friend of mine, because I thought I would attract bigger clients if I didn't operate under my name, and because a coworker of his had drawn a really cool picture of a snapping turtle, though in hindsight maybe not a great logo.
I won't claim it was the most thoughtful approach, but I'm sure names have been chosen for worse reasons. Probably. In my meager defense, I was young and figured I'd change it.
Ten years later I'm still using that name, though I still sometimes think about changing it. In that time I've learned a few important things you should consider before naming your business:
Don't underestimate people's ability to misspell a word like tortoise.
When choosing an animal, consider that aligning yourself with something that is slow and prone to biting people may not the best way to broadcast your services...
...but truthfully, after perhaps the first conversation, the name will probably never come up again, so don't sweat it too much.
If your business name consists of a few real words strung together that have nothing to do with your field, you may find yourself on the receiving end of some fantastic email solicitations such as this one: