I've always liked
Polly; partly I think because it was a family name, back in the 19th century, and senior relatives who remembered that
Polly spoke very highly of her. She was named after, I think, her grandmother who was
Eleanor Mary or
Mary Eleanor. Either way,
Polly was a nn for
Mary, not a name in itself.
The alternative would be
Molly, which I really dislike intensely in spite of a delightful Aunt
Molly, from the other side of the family. The parrot connection doesn't bother me one bit, perhaps because I mostly use human names for dogs and cats.
Given enough daughters, in an alternative universe, I think I'd use
Polly as a mn.
Tessa Juliet Polly rather pleases me!