Say, a monarch like Edward the Bankrupt, king of England or Charles the Silly, king of France. Did they know that people called them that, and do they say it right in front of him?
As always it depends on who you are referring to, but in general most of the epithets were acquired after the person's death. For instance even Charlemagne (Charles the Great) did not get "the Great" added until after his death, although it was rather soon after. Another example is Charles the Fat, who got his epithet roughly 200 years after he died. So that isn't a perfect answer to your question but in most cases I would say the nickname did not really exist yet.