When my younger daughter was about 9 months old, and going through the trauma of being required to sleep through the night, she attached herself to a stuffed dog. With our usual minimalist approach to naming things, this toy was named "Puppy". We have since acquired a backup called "Puppy's Sister", but Puppy reigns supreme to this day. Puppy is naturally somewhat threadbare, and stuffing-bare, and generally worn -- but is still recognizable and basically whole.
Our real live dog is now well past one year old, but we still tend to call her "the puppy" and to address her as "Puppy". She used to sleep in her crate in the guest room, but when we actually had guests coming for a change, we put her in my daughter's room, where she sleeps on the bed. The other morning, when I came in to wake girl and dog, Puppy was curled up next to Puppy. They looked very sweet together.