Since the Defiant wasn't named after Rod-Rod, I don't see where you're going.
I just said it was registered after his birthdate: NX-74205 comes from 1974, February 5. Rod Roddenberry worked as the art department production assistant, so in a way he had more to do with the ship than JJ’s grandfather did with the Kelvin.
What does that matter? It matters not at all. It's a great deal more interesting that people who work on these shows put their personalities and little points of commemoration - as well as in-jokes - into their creations than it is that all the marginalia can be shoehorned into some make-believe "history"...a history, BTW, that's knocked cockeyed over and over and over again whenever the production team decides that a thing they want or don't want to do matters more than obsessive continuity.
But the little things are supposed to remain little, in the background, whereas if you’re seriously looking for a Kelvin Day, something that would blow 0514 out of proportion, then it’s only natural to think in more in-universe terms.