My goal is to hang a suitable name on the protagonist that fits the story and the time. Page or Armor are more appropriate names for the pet of a knight than Fluffy. Also, use a name the audience can easily read. "Pfogmoregetti" might fit the character, but the difficulty of pronouncing it forces the reader to stop and focus on the name, rather than the action.
Characters give life to the story. Take time to know the character prior to writing. Focus on his/her uniqueness: hobbies, habits, fears, hopes, goal, temperament, vocal expressions, gestures, etc. A memorable character lives on in the minds of the readers after the book is finished.