Figure of speech. When Lenehan ends his limerick "I
can't see the Joe Miller. Can you?" he means that he
can't see the joke, since Joe Miller was a comedian. This
exemplifies the rhetorical principle of antonomasia:
substituting a property for a proper name, or vice versa.
Antonomasia (AN-toh-noh-MAH-see-uh, AN-tuh-noh-MAH-zhuh, and
similar pronunciations, from anti- = instead of + onomazein
= to name) is substitute naming. One form consists in giving
nicknames to people based on their nature, appearance,
occupation, or other properties: Shakespeare is the Bard,
Margaret Thatcher is the Iron Lady, Ronald Reagan is the
Gipper, Abraham Lincoln is the Great Emancipator, Bruce
Springsteen is the Boss, Napoleon is the Little Corporal,
Frank Sinatra is Old Blue Eyes, Maria Callas is La Divina, and
Elizabeth Warren is Pocahantas. The trick works also for
groups, fictional characters, works of art, places: the
Beatles are the Fab Four, Batman is the Dark Knight, Harry
Potter is The Boy Who Lived, Macbeth is the Scottish
Play, Beethoven's Third is the Eroica, Philadelphia is the
City of Brotherly Love, Rome is the Eternal City, Edinburth is
Auld Reekie, and Los Angeles is La La Land.
The principle can also operate in reverse: a miser is a
Scrooge, a ladies' man is a Casanova or Don Juan, a lover is a
Romeo, and a traitor is Judas. Gideon Burton
(rhetoric.byu.edu) cites a classical example: Multum
Ciceronis est in hac epistola ("There is much of Cicero
in this letter," i.e., much eloquence). Lenehan's "Joe
Miller" is antonomasia of this sort. Miller was an 18th
century English actor. After his death in 1738 his friend John
Motley published, under the pseudonym Elijah Jenkins, Joe
Miller's Jests, a collection of not particularly witty
witticisms, many of which had little connection to the
supposed source. Revisions and sequels continued to be
published well into the 19th century, and a familiar old joke
came to be known as a Millerism or, as in Aeolus, a
Joe Miller.
Antonomasia is so closely related to metonymy
that it might be called a sub-species of that trope. The term
periphrasis
occasionally is used in a synonymous sense, but its primary
meaning is much more general.