It is "Prompter" here. We sometimes have a person "on book" during rehearsals. Is the most grueling and thankless job in the theatre. You have to keep your nose glued to the script so if/when an actor call line you can help. Prompter can't watch rehearsal, laugh, interact,talk, nope, they are glued to book.

We call them script assistants. I just had the opposite situation. I was script assistant and the director kept muttering line under his breath if there was a millisecond pause before an actor spoke. It drove me crazy because more than half the time I could see that the actor was just about to start speaking. I asked the director when did he want me to stop prompting them (I'm used to the No Prompting Rule being used at least a week or two before the show goes on) and he told me to keep prompting for every rehearsal except the dress rehearsal. The two main characters had their lines down as did a couple others, but there were three of them that kept messing up consistently. No wonder their scenes were hit and miss every night of the run.