We have to identify the arrogance of Prince Prospero in thinking and believing so strongly that he can cheat or avoid death. One of the clear messages of this story is that death visits all, no matter how important, high or mighty we are and no matter what lengths we go to to try and avoid it. Therefore, there is a kind of ironic justification in the naming of the prince. Although he is clearly prosperous in terms of wealth, prosperity itself always comes to an end.
As a clue to his character, Edgar Allan Poe gives the prince a name that suggests wealth and success. He is described ironically as the fairy tale prince: happy and dauntless and sagacious. After "his dominions were half depopulated," those close to him are dead from the plague, he summons "a thousand hale and light-hearted friends" who are, of course, only "friends" because the mighty prince has summoned them. In addition, they may have food and shelter that may protect them from danger.
In his arrogance from having so much power and wealth, Prospero deludes himself into the conviction that he can wall out the deadly Red Death. But, even he, who approaches the unwanted guest with his power and wealth "maddening rage" and a dagger, falls victim to the "Darkness and Decay and the Red Death." For, no mortal man can ever defeat death.