What do you call a title that conceals a pun?

Solution 1:

When a real person has a name that is especially well suited or descriptive, it is called an aptronym (or aptonym)

A person’s name that is regarded as amusingly appropriate to their occupation: he began collecting aptronyms when he saw an ad for a flower shop operated by Flora Gardner

Also euonym

An appropriate or well-chosen name; (formerly in technical use) a name that conforms to the requirements of a particular system of nomenclature. The term was popularized by its appearance as the winning word in the 1997 U.S. National Spelling Bee competition.

Oxford Dictionaries Online

A long list of such real names is found in this Wikipedia article.

The fanciful versions seem to be a logical extension.