What next, Spiro Agnew?
Actually, the men with that name had some pretty impressive accomplishments.
The first Adlai was Vice-President during Grover Cleveland's first term. The name skipped a generation to his grandson Adlai II, the best known of the bunch. He, of course, ran against Eisenhower and lost twice, but as UN Ambassador he's remembered well for busting the balls of his Soviet counterpart during the Cuban Missile Crisis (which would of course inspire that scene in ST6). Adlai III was a US senator from Illinois throughout the 1970's