adding name to book

[mdray]

During halftime, scorer informs official that A6 played in the first half, but his name is not in the book. Official realizes scorer is correct and instructs scorer to add the name and begins the second half with a T on team A. Is the official correct?

Can an official direct that the name be added to the book in this situation?
If A6 had not scored or committed a foul during the first half, does that alter how the official should handle this?

The infraction, that must be penalized when it occurs and prior to the ball becoming live, is the act of adding the name to the book. If the coach says A6 will not play the rest of the game, does his name have to be added to the book?
(I seem to remember an old case play related to this, but haven't been able to find it)