that's brilliant ...
was 'er old man a diamond geezer ...
I guess she was an only child ...
The thing is, it's the people who are posh/rich/MC or UC, not the names.
I know two girls called Willa - not a name I think of as 'posh'. One of them is plenty nice but called Willa b/c her parents liked it.
But the other one is v. posh but v modest. Willa is a shortened version of her old fashioned, passed down, distinctive (possibly outing) family name. Her older relatives (aunts, gp's) were good friends with Queen Elizabeth and Prince Philip and were close to King Charles when he was a boy.
And think of the name Harry. That boy could be a prince of the realm or a chimney sweep or anything in between.
Lots of the posh/rich/UC/MC boys I know have a traditional name and use the short form: Freddie for Frederick, Eddie for Edward, Charlie for Charles. Girls often have similarly traditional or straightforward names: Emma, Ella, Louisa, Alice, Florence, Chloe, Sophie. Some are more interesting: Esme, Aurelia, Arabella, Cosmo, Humphrey, Jasper, Ottilie, Eva/Evie, Oscar