Do first and last name go together?

Kelly
We're struggling with naming our second boy, due in 3 weeks! The trouble is our last name is Skinner, and we like a lot of names ending in an "s", and I don't like the way the names aren't broken up when said together. But then we also like some names ending in "er", specifically Cooper, and can't decide if that's too much with a last name ending in the Dave sound. I have said Cooper Skinner to myself a million times and still can't decide. So I'm asking you all for your opinions! My only other name I can decide on right now is Owen, bit I'm not sold there yet either. Our first son is Bennett.