I had about 10 little ID books the same, with customer's names in (sometimes Membership Numbers too) when I worked at the Vic.
It could be a reservation book but more likely an ID book for when punters came in and names were needed for the sheets we tracked their cash drop, win/losses etc.
Another good use for roulette cards if the Inspector didn't want the books in their (inside) pocket as they were used instead. I used to go home most nights with more names to put inside them.