Fame in Monster Rancher 2 is how popular your monster is. 1 is the lowest fame and 100 being the highest. You can get more fame by winning battles or eating Star Prunes. But your fame will go down if you enter a battle that is below your regular rank. And also fame may help you get certain monsters, like Dragon or Wracky. And people like Dr.Talico, visit you if your fame is high enough.