Well, the classical names are what people like that are most likely to use for their kids. Frankly I do't see such people naming boys
Knox or
Xavier. Maybe
Knox if it's a family name, but not
Xavier. If they were younger parents, or less "blue-blood" and more "nouveau-riche" yes, but not as you've described them.
Also, a man born into such a family in the fifties would be very likely to bear a name already established in his family, or just be a
Junior or a IV or something.
William makes perfect sense for him.
His wife might not be an
Anne or an
Elizabeth, but again, she likely would not have a name that's atypical of her time.
Diane,
Barbara,
Linda,
Susan,
Pamela,
Patricia,
Carol,
Karen,
Eileen...
The daughters might have names considered very popular today, like
Chloe,
Emma,
Sophie,
Amelia,
Julia or
Lucy. They might have family surnames as first names, but they likely wouldn't be named
Ashley or
Mackenzie purely for the sound of it. They'd be likely to have a "family" first name, whether it's say,
Mackenzie, or Grandma
Harriet's name, and then go by the middle name.
It's likely one son would be named after his father, grandfather or uncle, again possibly going by a middle name.