THIS MIGHT SURPRISE YOU
The answer
Disagree. The Talmud, from the 500s AD, does name Samuel as author of the parts before his death. Drawing on 1 Chronicles 29:29, it names Nathan and Gad for the rest. But Samuel dies at 1 Samuel 25:1 with most of the two books still ahead, and the records of Nathan and Gad are known nowhere else. Scholars read Samuel as built from works written later in the monarchy and edited while Judah's people were exiled in Babylon.
Why it’s interesting
The note on 1 Chronicles 29:29 in the New Oxford Annotated Bible says it is unclear whether those records ever existed. It sees the link to these prophets as one more way Chronicles raises David's standing. The Story of David's Rise, one of the works scholars find in Samuel, was most likely composed in Judah after the northern kingdom of Israel fell in 722 BC.
Scholarly consensus
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