If we still did it by firing squad or hanging, then yes I’d want it broadcast. Public lethal injection wouldn’t have the same visceral deterrent effect; it’s just a guy going to sleep and a physician confirming death (which, sadly, people witness in hospitals every day). You only hide what you’re ashamed of, and there’s no shame in carrying out a just punishment.
I don’t think the death penalty really has much of a deterrent effect. People have been murdering others forever, and so far, nothing seems to stop them. I think it should be done with no more fanfare than stepping on a cockroach. He doesn’t deserve to even have his name mentioned after the death sentence is declared.