Usually, it would be correct to use the definite form. We know that we're talking about a specific Polish King, whose name was 'Casimir the Great'. When you know that you are referring to a specific person or item, or something that is unique (like the Sun) you would use "the". Unless we know that there are a ton of 'Casimir the Great's, we would use "the".
In case we're not talking about a specific item, or we're introducing an object for the first time in a conversation, you would use an indefinite article, like "I want an apple." If you wanted a specific apple and the other person knew which apple you were talking about, you would say "the apple".
Think of it this way. Definite articles are when you are speaking about something definite, or something exact or defined (just my own little tip for remembering). Indefinite articles are for something that is not declared, or unspecified. In certain contexts, you might find people using an indefinite article before a proper noun, and that's when there might be more people or things with the same name or identity. I remember an occasion when my English teacher said that there was a certain graveyard with records of "a William Shakespeare" or something of the sort. But for your given example, I believe it would be most appropriate to use a definite article.