In the second draft script of "Prime Factors", Janeway's dog was named Oakley and was said to be a golden retriever.
As evidenced by the first draft script of "Flashback", Mollie was originally to have appeared in that installment, in a memory of Janeway's. However, all mention of the dog was eliminated from the episode by the time the final draft of the script was issued.
The novelization of the episode, p.20, named this dog "Bear" instead of Mollie. The script for "Shattered" spelled her name as "Molly".