I think Jackson, Jax are perfect. Love Barney too.
Max was going to be Winston, Winnie. Dad looked at the puppy picture and said the name didn't fit. He chose Max, and I agreed if it could be Maximus for Russel Crowe's character in Gladiator. Our Italian neighbor called him Maximo and it stuck. We call him Maxman mostly.
Whenever Max is exhibiting his intensity, I pick him up and cradle him like a baby, and tell him we should have called him Winnie so that he would be mellow.