Who is Mr. July? Is this an epithet, or idiom, or...? And how do you use it?

Well ... in a calendar with pictures of a different woman or man for each month, the person whose picture is used for a particular month will be called Miss (or Mr.) January, February, and so on. So "Mr. July" is the man whose picture is used for the month of July. Is that what you mean? In that case, it would just be a cultural-specific expression.