My first whippet was called Felicity but I called her Fliss ( although I usually like my dogs names to finish in ee) or Flissety. I know a little dog called Missy: I quite like that.
I do like a dog to have a 'proper' name. A neighbour's dog is Dave - another has a Stanley. I like Daisy - your puppy looks so lovable, I hope you have many happy years with her.
My friend has a dog called Stanley and another a Labrador called Bryn (he was from Wales) Honey or Hope are two more that spring to mind for Fannies pup.
Our adorable little rescue cats had a mummy called Mimi who got adopted before we adopted them. She was a beautiful little street cat, we saw a picture of her. She survived and gave birth to our wonderful calico twins and I am so glad someone took her home.