The book does not name one author
Unlike some of Paul’s letters, 1 Samuel never introduces a named author. It tells the story of Israel’s shift from judges to kings, following Hannah, Samuel, Saul and the young David, but it does not tell readers who arranged the whole account into its final form.
That means the most honest answer is simple: we do not know the name of the final human author. The book itself points readers beyond its writer to the Lord, who was at work in Israel’s history.
Why Samuel is linked with the book
Samuel was a prophet, judge and spiritual leader in the first part of the story. He also wrote down matters concerning Israel’s kingship when Saul became king, showing that he did produce records during this period (1 Samuel 10:25).
Still, Samuel could not have written every part of 1 Samuel. The narrative records his death and then continues with Saul’s pursuit of David and David’s time among the Philistines (1 Samuel 25:1; 1 Samuel 27:6). So Samuel may have supplied early source material, rather than being the sole author of the finished book.
Then Samuel told the people the manner of the kingdom, and wrote it in a book, and laid it up before the Lord. And Samuel sent all the people away, every man to his house.
Nathan and Gad may have contributed
A later Bible passage gives the strongest reason for the traditional view. While describing David’s reign, 1 Chronicles says its events were recorded in the words or records of Samuel the seer, Nathan the prophet and Gad the seer (1 Chronicles 29:29).
This verse does not explicitly say that those three men wrote the biblical books now called 1 and 2 Samuel. But it shows that prophetic records from all three were known and valued. Many readers therefore understand 1 Samuel and 2 Samuel as drawing on material connected with Samuel, Nathan and Gad.
Now the acts of David the king, first and last, behold, they are written in the book of Samuel the seer, and in the book of Nathan the prophet, and in the book of Gad the seer,
An unnamed compiler is likely
The book includes comments that look back on events from a later point in time. For example, it notes that Ziklag belonged to the kings of Judah “unto this day”, which suggests the narrator wrote after David’s earlier life (1 Samuel 27:6).
So it is reasonable to picture an unnamed inspired writer or editor gathering trustworthy accounts and shaping them into one continuous story. Scripture does not satisfy every curiosity about the process, but it does present these records as part of God’s word for teaching and hope (Romans 15:4).