Not meaning those with more jovial names (I'm sure there was a French King known as "The Fat") but those who had more nasty nicknames - Ivan the Terrible, for example, would suggest that he wasn't the sort of chap you would go around calling Terrible while he was still alive so I would have thought that a nickname that insulting would only come into effect once said monarch was dead and not around to effect retribution for the insult.
Had a look in the FAQ and couldn't see one exactly answering this in the monarch naming section so hope this is a relevant query
Ivan's "Terrible" is in the now archaic sense of "Inspiring terror". "Ivan the Terrifying" would be a more accurate translation of "Ivan Grozny", which is what he's known as in Russia. So in fact it's not at all a negative name.
In his lifetime, William the Conqueror was better known as William the Bastard. Not to his face, I suspect, but it's an instance of his nickname being improved historically