It can be “any” book. I’ve seen many variations.
At the top of the list, I’ve seen pre-printed books with nice covers made specifically for that purpose. I’ve seen these in religious goods stores/catalogues but they’re not easy to find.
At the other extreme, I’ve seen just simple “blank line” or “record” books from stationary stores or even student notebooks. The last one just looks cheap.
We use (1 at each location) hardbound books that are plain blank lines on the inside while the cover has the church names stamped on them along with the words “Faithful Departed” The inside has nothing but names: no dates or other comments.
The book only needs to have blank line–no columns, just lines. I’ve even seen completely blank pages, but don’t recommend it because people will write in different sizes and it looks disorganized or maybe “messy” might be a word. Lots of wasted space.
Over the years (being transferred a few times) I’ve had several occasions to order these for the parish. They’re not expensive. Here’s one example www (dot) bookfactory (dot) com. I’m only posting that to illustrate how easy it is to order such a book. No endorsement implied.