Hmmm, I don't know if you can generalise about 'posh/toff' names any more than you can when people ask about 'chav' names.
Instinctively, I would give the stereotypical answers of Rupert, Montgomery, Ptolemy etc too. But, I'm not convinced that's actually reality (well, there might be a general correlation between some names and social class but there are also too many exceptions to be able to call them exceptions.)
I've worked in a 'posh' school for 10 years. We've had boys called:
Ptolemy, Sebastian, Frederick, Jason, Dylan, Gavin, Rupert, Cosmo, Darren, Connor, Orlando, Lysander, Hugo, Zak, Hughie, Wilkie, Alfie, Jonty, Riley, Montgomery, Rafi, Bailey, Maximillian, Jordan and Ferdi. Plus plenty of others that are usually categorised one way or the other. Of course, the majority have been called James, Samuel, Daniel, Oliver, Oscar, Noah, George and Thomas, just like everywhere else.