Interesting. I think "internalizing song names" is one way to put it. In general I often have trouble associating song names with the music. I think that's how my memory works (or doesn't). Don't think working on it will do much, but even the most minimal cheat sheet fixes it. It's like cueing actors, once the cue person whispers a word or two, the rest just flows.
I have the problem IMHO because I don't pay attention to the lyrics. But putting in the effort to associate the song title with recognizable elements of each song does work and it gets easier with practice. Essentially you need to develop a new skill.
Cheat sheets can be useful, but they become less effective as you learn more songs. Imagine what it will be like when you know 100 or more songs and need to be able to start playing as soon as a song is called. You don't always have the benefit of a music stand on stage to hold your notes, and the stage is not always lit well enough to read.