Hello, Dolly! Okay, we couldn't resist, but be warned: Most people who meet your little Dolly won't be able to either. This nickname-name, rarely heard since whatever decade Dolly Parton was born, is singing a fashionable note again along with sisters Dottie and Dixie; it was chosen for one of their twin girls by Rebecca Romijn and Jerry O'Connell.
Dolly has been used on its own since the seventeenth century, so common then that it became a generic term for a favored girl. In the US, Dolly was a Top 300 name around the turn of the last century. The fourth First Lady of the United States spelled her name variously as Dolly and Dolley Madison. And of course Dolly Levi is the name of the central character in the iconic musical bearing her name.
Trivia tidbit: Dolly, the sheep that was the first mammal to be cloned, was named after Dolly Parton.