Jo reggelt kivanok, Peter -- is wrong because "kivanok"?
It should be correct. That's the most polite way to say it.
That would be: "I wish you a good morning, Peter"
Just, hungarians don't speak without the word "KIVANOK" I know about it
It's correct with or without kívánok as well. It's just a matter of politeness.
Jó reggelt Péter
It is written Peter, not Péter