Well, in 1947, theaters were naming cartoons in their programs, namely the Little Lulu "A Scout with the Gout" abbreviated to "Scout with Gout" (with the Red House and Blondie Knows Best) and the Friz Freleng Bugs Bunny short Rabbit Transit (with Suddenly It's Spring and The Devil Thumbs a Ride). Images from eBay.
Several programs from the Mission Theater in Los Angeles from around 1934 cropped up on eBay; they mention when there's a cartoon (it's not actually every show), and the cartoons are entirely anonymous; except when it comes to one example where instead of cartoon they say "Mickey Mouse". Happy public domain Mickey Mouse day!
