The book of Esther.
Surprisingly, the book of Esther does not mention the name of God at all.
There is not a version of the bible that doesn't mention God in the book of Ruth. However, God is not mentioned in the book of Esther in every version.
Esther is the only Bible book which doesn't mention God specifically. Ruth does mention God at Ruth 1:16 Song of Solomon mentions "flame of Jah/the LORD" LORD in capitals being the 'placeholder' for God's name
The whole Bible is inspired of God as mentioned at 1 Timothy 3:16. God's name is mentioned about 7,000 times in the original text of the Hebrew Scriptures. Jehovah God himself directed Bible writers to use his name. For example, he inspired the prophet Joel to write: “Everyone who calls on the name of Jehovah will be saved.” (Joel 2:32) And God caused one psalmist to write: “May people know that you, whose name is Jehovah, you alone are the Most High over all the earth.” (Psalm 83:18) The name Jehovah is missing from many Bible translations. The reasons for this vary but it was replaced with titles such as "Lord" or "God". But we can conclude that there is no book in the Bible that does not mention God's name. (New World Translation of The Holy Scriptures)
Esther. And the reason is because the Babylonian exile (during which it took place) was a fulfillment of the prophecy that God would conceal His countenance (Deuteronomy ch.31).