I haven’t been able to recall any specific word for ‘rep list’ or ‘rep book’ that stands out in memory. If such a word exists, I am almost certain to have heard it, but I cannot recall any special one. I use “my rep list” or “my book” and bands I have played in use “rep list” and make up “set lists” for individual shows, and “sample set lists” to gain bookings. Technology has made making a DVD easier than presenting a paper list, though some of the older folks who book for their venues still like to see paper.
There is the term, ‘The Real Book’ and also the term, “fake book” as in ”a fake book.” These are both books of lists of musical information that allow a musician to “fake” knowing the material. That is to say, a “fake book” gives a competent player enough information to create his part in a manner that should be unperceived by the audience, while performing live, on-stage. Sometimes chord names will be called out (or whispered) such as “OK, this is a C A-minor F and G, but in the key of ...” Mostly, before the show, if there is time, notes will be scrawled on a piece of paper maintained in a discreet location, or even taped to a mic-stand if the show is ‘casual’ enough to allow this.
The term ‘The Real Book’ originated at Berklee School of Music (late 1960’s, early 1970’s?), students there made their own chord charts for nearly all jazz standards. These ‘charts’ were passed around for many years and copied eventually by musicians outside of Berklee. At one point, nearly every performing musician had a version of “The Real Book.” There were errors, copyright issues, and poor quality issues--i.e., many entries were handwritten or transcribed, often faultily, from handwritten notes.
To me, the term ‘fake book’ means a usually large, usually purchased book or looseleaf set of pages or cards listing in a kind of musical shorthand many songs or pieces of varying genre, such as Rock, Folk, Country, Metal, Funk, etc. Wikipedia offers:
...A fake book is a collection of musical lead sheets intended to help a performer quickly learn new songs. Each song in a fake book contains the melody line, basic chords, and lyrics - the minimal information needed by a musician to make an impromptu arrangement of a song, or “fake it.”
The fake book is a central part of the culture of playing music in public, particularly in jazz, where improvisation is particularly valued.
Fake books are not intended for novices: the reader must follow and interpret the scant notation, and generally needs to have thorough familiarity with chords and sheet music....
The term ‘Book’ or “My Book’ is an individual artist’s rep list, the songs or pieces known by the musician whose ‘Book’ it is. Generally, it is comprised of only minimal information and hand-written in a shorthand tailored to the individual musician and instrument(s).
Entries in my book are as abrupt as:
Ed’s opening 12-bar
I IV V
I, I, I, I
IV, IV, I, I
V, IV, I, I
I III V VI IIX—↑↓
Such an entry allows the key to remain unspecified and therefore the information remains applicable over all keys rather than only for a single key which would be the case if notes (such as for the ‘key of A’: A D E - instead of I IV V) were specified. And actually many entries are even more terse, such as “King’s Crow/ 130bpm B A D E X3 - G C solo on D-E” all handwritten for the most part; parts I have digitized end up being hand-marked and drawn on and written on pretty quickly.
I cannot recall any special word for “my [rep] book” or “our [rep] book”. I have heard “my kit” but I don’t think that’s likely to be the one the OP is looking for.