Well... Wuthering Heights got away with it! 
I imagine if you treat it as you said, with most people calling them by nicknames, it'll work. Names are pretty flexible, and I imagine a lot of the time, the senior one will be called "Sir" or "Dad" or "Mr. [Name]", while the younger one might get called "Junior", "Kid", "Bernie", "Son", "Boy".
Another common thing in families with inherited family names, is that the younger goes by their middle name as their daily use name. Or the middle name gets used to differentiate that person from others. So Bernard Junior, if his name is say Bernard Edward Smith, might go by "Eddie" most of the time, and people might be surprised to learn his first name isn't the one he uses. My partner actually grew up being called their middle name by their family, and eventually changed it legally in the end.