Got your classical right here. “¡Adelita!” composed by Francisco Tárrega.
In addition to Sunny and Windy, there’s also Stormy.
Lalena (The “n” is supposed to have a tilde over it)
Adalida - George Strait
By the way, the song “Anna” actually has a parenthetical subtitle … the complete title is “Anna (Go to Him)”.
Juanita (Men of the Robert Shaw Chorale) (another version)
Venus - Shocking Blue; later covered by Bananarama
Cymbaline (Note: The lyrics don’t make clear whether this is a woman or a man. Cymbeline, the Shakespeare play, is about a king of ancient Britain.)
“Rosalita”
What, no Rhiannon?
An oldie and goodie from down Mexico way—“Sandunga”
Y una otra—“Naila”
“Isis”
This “Fancy” certainly is a girl’s name. Reba sings it OK, but this is the original by Bobbie Gentry, who wrote it.
“Victoria”
“Lily”
Technically, it’s “Rosalita (Come Out Tonight)”, so I will flout the rules and mention “4th Of July, Asbury Park (Sandy)”. 
Closer to the rules, his Bobby Jean.
Sandy - from Grease
You want classical? Okay.
Nicolette - #1 of Trois chansons by Maurice Ravel.
Sugaree