Ragdolls are so floppy and easy going, they need a name that feels cozy and kinda boring, like
Andy or
Maggie or
Marsha or
Duncan.
For a more elaborate name I'd head into the realm of something so hifalutin it's silly, like Perlipat or
Huckleberry Finn or
Judah Ben-Hur or Zinfandel or
Jehoshaphat.
Something food related would be cute. Like Quiche or Rutabaga, or Strawberry Pavlova, or Croquette.