Do any Waco aircraft have model names?
Waco Aircraft was originally called "Weaver Aircraft Company of Ohio" in 1919. The first Weaver Aircraft Company aircraft was the 1920 "Cootie" but was it also called the "Waco Cootie". It was a monoplane that crashed on it's first flight and then rebuilt as a biplane. 

The aircraft designs were called "Waco" as in "Waco 9" "Waco 10" even though the company became "Advance Aircraft Company" in 1923. In 1929 the name was formally changed to "Waco Aircraft Company".

The last Waco production aircraft design was the E Series "Aristocrat" biplane. There was also one prototype Model W "Aristocraft" which was a pusher prop, monoplane.  All the other Waco types had model designations consisting of letters and numbers, or military designations.