Plenty of upper- and middle-class babies with unique, or at least unusual, names.
Such as?
In my experience, upper and upper-middle class kids get common names, usually a bit on the conservative side, nothing that sticks out too much. Never crazy spelling, never unique names.
https://www.theguardian.com/politics/2017/jul/05/jacob-rees-...
Interestingly the article shows a way for upper-class people to signal upper-class-ness through names. The other kids all have a normal given name, and can easily fly under the radar. But once you start saying all of their first names, it's a clear signal.
(Because it is in line with how many European royals name their children.)
X Æ A-12 Musk?
Never say never.
There is a big difference between uncommon names but with deep roots like the above mentioned Sixtus and completely unique names X Æ A-12.
The former is very common in the upper classes, the latter not so much.
Here's a good resource if you want to read up on how class works in the US: https://siderea.livejournal.com/1260265.html
Moon Unit, Dweezil, and Diva Thin Muffin Zappa.
Raddix Madden
Lyra Antarctica Sheeran
Kal-El Coppola Cage
Pilot Inspektor Lee
Blue Ivy Carter
Rosalind Arusha Arkadina Altalune Florence Busson
Aleph Portman-Millepied
Bear Blu Jarecki
Kulture Kiari Cephus
Sparrow James Midnight Madden
Exton Downey
Seargeoh Stallone
North, Saint, and Chicago West
Rumer, Scout and Tellulah Belle Willis
In the usual sense used in the US, they’d mostly be above the upper middle class and into the upper class.
In the more theoretically grounded system otherwise used when discussing capitalist societies, they’d still all be, at birth, be at least petit bourgeois, so the idea that such names are clear indication of membership in the “lower classes” is only even possibly true of capitalist classes in the narrowest possible sense (“not of the haut bourgeoisie”, though even that is a stretch), or maybe if you are speaking of vestigial pre-capitalist class systems, and still just as narrowly (“not the titled nobility”).
Also, the number of people who hate their "unique and quirky" name they got from their parents is much, much, much, much higher than the number of people who hate their normal name.