This is one of those names where I have to break it to you.
The name is really a phonetic version of the Dutch last name “Schuyler,” courtesy of all the old Dutch settler surnames and place names in the state of New York. It’s an occupational surname. It means “scholar,” and is not anything at all about the sky.
On the bright side, this means that you’re totally covered for baptismal names and patron saints, no matter whether it’s a boy or a girl.
“Scholar” or “schooled one” in Latin is “scholasticus.”
So for girls, the patron saint would be St. Benedict’s famously learned and stubborn twin sister, St. Scholastica. She is a great saint! Her feast day is Feb. 10, and she was traditionally held to be a patron of students (especially in Oxford), and of all Benedictines and nuns, as well as against storms, rain, and thunder (she prayed for bad weather to keep her brother at her convent so they could talk further, and the Lord did it for her, much to Benedict’s irritation), and against rabid dogs and childhood seizures.
There are several male saints with the title Scholasticus in their nicknames. The main one is St. John Climacus, a monk and author of an important mystical treatise called the Ladder (Klimakos, hence his better-known nickname).
There’s also a Benedictine monastery near Subiaco that’s called “St. Scholasticus,” but it’s named after St. Scholastica. Several Benedictine colleges throughout the world are named after the monastery. You can name kids after monasteries and holy sites, too, so that’s another way to go.
UPDATE: With the popularity of the Schuyler sisters in the musical Hamilton, the name “Schuyler” might have another comeback as a girl’s name. With that spelling, even. But… they weren’t exactly saintly, and they decidedly weren’t Catholic. So if you’re picking a Catholic girl’s name, keep that in mind.