Most old money folk tend to have timeless "classic" names which would also not cause surprise when they crop up in other classes (albeit less commonly). These are often names which feature in royal families across various generations.
So for girls:
Alexandra, Elizabeth, Catherine, Victoria, Charlotte, Eleanor, Beatrice.
Boys:
Edward, George, Henry, William, Charles, Alexander, Thomas, James.
If you want something a bit more unusual I've put some suggestions below. However the risk with those names is that they might suddenly catch a trend and become rapidly declasse. This is harder to predict than the classic names.
Girls: Antonia, Leonora, Helena, Camilla, Portia, Vanessa, Cassandra, Felicity, Rosamund, Juliet, Araminta.
Boys: Benedict, Randolph, Oswald, Peregrine, Sebastian, Fabian, Montague, Tristram, Tarquin, Hector, Julius/Julian.