Part historical fact, largely urban legend. Once upon a time, they used to read the names of all arriving pilgrims at the noon Mass. Many people incorrectly believe this practice continues. The person you referenced in your post might be referring to those lists of names from years long gone by.
As the numbers of daily arriving pilgrims grew, they merely announced how many from which countries. This was my first memory, when I completed my first Camino in May 2013.
Presently, and as the daily pilgrim arrival volumes can (and does) exceed 3,000 during the peak season, at the noon Pilgrim Mass, they merely mention the countries the arriving pilgrims originate from.
However, there never was "a book," at least insofar as I know. The closest thing to a formal record was the single page form that each pilgrim completed one line on. It was / is called "the Estadillo." It merely captures the information needed to issue the Compostela and for management purposes.
As part of the COVID response to limit viral infection vectors, they converted this paper form to an online submission method, via your smart phone. You do this before you arrive at the Pilgrim Office.
Management has a reasonable need to know how many of what sort of Pilgrim is arriving. So, things like: national origin, native languages, age, professions, folks who are secular or who might be religious, all contribute to the Pilgrim Office and Cathedral management doing a better job of providing arrival services to Pilgrims in future. It is not a perfect science - more of an art really. But, they do analyze these data - mostly in the off-season.
Hope this helps.
Tom