Also not really an aristocrat, more like an upper-middle class banker's family. The "von ..." was more of a faux title, although his family did have an honorary nobility title (a different one) received a few decades before.
In europe -every upstart family, at some point tried to get the "von und zu","van", "de" only exemption from this is the english aristocracy.. were you glue a "lord" or "lady" in front of the name, instead of a addition bewetween name and surname.
Usually Von Neumann is thought to be Hungarian. Born in Budapest, which at the time was part of the Austro-Hungarian Empire.