Lots of dogs named Molly, too. Everyone must think they're being so original or something naming their dog Molly and they're being anything but. I don't really like Molly, but if I did, it would ruin it for me.
Yes, Molly is very common, too. Any cutesy human name fits, it would seem. Lucy, Molly, Sally, Rosie, etc. I've noticed the Ava trend with human babies was mirrored with dogs, too.