Well, you can always run from a wild Pokemon, but if a trainer finds you, you won't be able to back out. Besides, he's not gonna grow any stronger that way. And if he looks like he's getting kinda weak, you can always use a Potion or feed him a Berry, and he'll heal up right away!

And you don't necessarily have to name him, but, it's something people usually do. A friend of mine told me not doing that would be kinda like calling a dog, well, "Dog".