At the low stats that pets are born with, every (or nearly every) level of a stat has a name. BD stats don't get interesting though until you're beyond that. The numbers (listed at the training schools or battledome) are what's important, not their descriptions.
Your pet's stats don't change as your pet ages, you'll have to train them for that at the
Mystery Island Training School or the
Swashbuckling Academy on Krawk Island. A visit to
Coltzan's Shrine may pay off too for low level pets.
Good luck in the Battledome!