When we registered our Sully, we made his registered name very "official" sounding.
My husband is a WWII buff and so that's partly how we chose his reg. name. Plus, we were married on Sullivan's Island... His reg. name is "General Montgomery Sullivan"
You could make Muffy a "Little Miss Muffy" or "Yourname's Muffy Girl" (Sully's mom was Matt's Tiny Girl, they called her Tiny...she was 7lbs, lol.)
Princess Muffy — Our Darling Muffy — Our Sweet Muffy-Girl
Think of what you'll call her as a pet-name and go with it. In the end, it doesn't reeeeally matter anyway. It's just fun to come up with something "for the books."
