Cordelia, the name of King Lear's one sympathetic daughter, has style and substance, and is exactly the kind of old-fashioned, grown-up name that many parents are seeking today. If you're torn between Cordelia and the equally lovely Cora, you can always choose Cordelia for long and then call her Cora for short—or Delia, Lia, Del, or even the extremely different Cordie. Cordelia is a Nameberry favorite—Number 106 on the site—and it reentered the US Top 1000 in 2014 after a 60+ year absence.
Cordelia also appeared in Evelyn Waugh's Brideshead Revisited, Margaret Atwood's Cat's Eye, as detective Cordelia Gray in P.D. James's mystery novels, and was promoted by a character on both Buffy the Vampire Slayer and its spin-off Angel.
And then there's that quote from the heroine of Anne of Green Gables: "I would love to be called Cordelia. It's such a perfectly elegant name."