Originally the two books of Samuel formed o n e historical book. It was the translators of the Septuagint (Greek translation of the OT at about 200 BC) who separated the book into two parts. Henceforward the first book ended with Saul’s death and the second book started with David’s reign.
From the Septuagint this separation into two books was taken over into the Vulgate (Latin translation of the whole Bible in the 4th century AC) and finally since Daniel Bomberg (1517) also into the printed editions of the Hebrew Bible.
In the Septuagint as well as the Vulgate the books of Samuel are considered as part of the books of the Kings. This title is not altogether unsuitable for in the books of Samuel the kingdoms of Saul and David are described and in the books of Kings the reigns of Israel’s and Judah’s monarchs.
And yet the original Hebrew title Samuel is more appropriate for both books describe the life of Samuel the prophet as well as the lives of the two kings who were anointed by him.