From The Heavenly Book Motif in Judeo-Christian Apocalypses by Leslie Baynes:

Malachi’s attribution of a book of remembrance to the Lord suggests an important theological question that may be directed to heavenly bookkeeping in general: what sort of god is it who requires written reminders?Nowhere does ancient Jewish literature even hint at asking such a question; evidently it is not something that attracts anyone’s attention. The background of the idea that God uses a reminder book, however, is not too hard to guess: most probably it is an anthropomorphism, an extension to God of a characteristic of rulers, or at least their officials, who use books and writing to keep administrative records (i.e., Ezra 6:1–5; Esther 2:23, 9:25,32). But while the Jews appear never to have looked askance at a God who uses written records, some Greeks did.