K.P.
I wouldn't think you would want to name your two sons the same thing. I'm a 5th generation Katherine, and my other siblings' names certainly aren't all Katherine lol. That would get confusing! If you want to stick with the family name thing, maybe there is another person in your family whose name you could carry on?
In the end though, one of the joys of creating, carrying, and then giving birth to a child, is that you can name it whatever you want! Good luck and congratulations!