Sefer Shmuel Introduction
Although Sefer Shmuel appears as two seforim nowadays, (Shmuel Alef & Shmuel Beis), they are really one sefer; written by the nevi'im Shmuel, Gad and Nassan. The sefer deals with a crucial one hundred years (approx) in the history of Klal Yisrael - the transition from the period of Shoftim (judges) to those of the Melachim (kings).
The roles of 'melech' and 'shofet' are similar in many ways - they are both in charge of war, appointed by Hashem via the Sanhedrin...etc. However, the Abarbanel notes some differences; only a king is anointed with special oil (shemen ha’mishcha), a king has greater jurisdiction in national issues than a shofet, and a king has special laws which apply only to him (e.g. no-one may ride on his horse, he may not get drunk, have too much money, wives or horses). Finally, a king may set special taxes and his son has the right to become the next king (if worthy). The shofet is not subject to these laws. This transition occurs during Sefer Shmuel (paralleling this transition is Megillas Rus which starts וַיְהִי בִּימֵי שְׁפֹט הַשֹּׁפְטִים and ends with the birth of King David) under the guidance of the final shofet – Shmuel Hanavi, and thus the sefer is named after him.
If Sefer Shmuel is the transition between the reign of the shoftim and the melachim, why is the section of Sefer Shmuel about the last shofet, Shmuel, placed at the end of Sefer Shoftim, and the sections about Shaul and Dovid, the kings, written in Sefer Melachim?
The Abarbanel writes that the reason why Sefer Shmuel is a sefer in its own right is because it is an accolade and tribute to its two main stars; Shmuel HaNavi, the greatest shofet, and Dovid HaMelech, the greatest melech. Dovid is not merely the first king, he is the beginning of a line of Kings which will continue throughout history culminating with Moshiach.
But our question about the name of the sefer returns; if the focus of the sefer is Shmuel and Dovid, why doesn't the name boast both names? 'Sefer Shmuel v'Dovid'? The Meforshim answer that a sefer can't have two names and Shmuel was given the title over Dovid because of his kedusha which he had from the start of his life, as well as his great level of prophecy - in whose merit B'nei Yisrael were given many other prophets.
So who was Shmuel?
Shmuel was from the tribe of Levi, and he successfully managed to get the entire nation to accept Hashem’s yolk (ohl malchus shamayim) with love and fear. This was a particularly great achievement due to the fact that the sefer opens with the story of Elkanah, Shmuel's father, and his annual trips to the mishkan. Elkannah went out of his way to travel through many cities on his way in order to get people to come with him to the mishkan for the yomim tovim. We see that the people were lax in the mitzvah of aliyah le’regel at the start of Shmuel’s reign, yet Shmuel turned this around. Shmuel was a nazir (Rambam), and he is called ’the teacher/master of Neviim;’ he even established a Beis Midrash for Neviim. Unlike other leaders, Shmuel went to the people as opposed to waiting for the people to have to travel to him. Thus, he was constantly moving about from place to place. He had a beis din which had ru’ach ha’kodesh, and he oversaw a proliferation of Torah knowledge amongst the people in his time. Apart from prophesying, anointing Shaul and Dovid, and being their mentors, Shmuel wrote Sefer Shoftim and part of Sefer Shmuel. In Tehillim 99, Dovid Hamelech compares Shmuel to no less that Moshe and Aharon.