Yorkshire Terrier called Bear because the breeder had nicknamed him, and it stuck because of how very teddy bear like he is. Then there's the Labrador Bess, who was three when we got her so naturally kept her name. Misty, who is about ten different breeds of dog, was six when we got her and again kept her name. George is a Bassett Hound named because he was born on St.George's day.
The cats are Olivia, Harry and Treacle. Olivia, or Livvie, was named because my Gran had wanted to call a daughter that but never had another girl, Harry is short for "Harry the Spider" which comes from his ability to sense a spider three rooms over, and Treacle was another rescue who was already named.