This is discussed, of course, by Abarbanel, first thing in Sefer Shmuel.
An initial glance at the names of the books of Tanach shows us that the books are not necessarily named for their authors, especially in this case being that Shmuel clearly did not author a large portion of Sefer Shmuel. Rather, books are named for their content.
There are two ways to look at the overarching theme of Sefer Shmuel that would explain the choice of name for this book:
- The life and accomplishments of Shmuel Hanavi. Clearly, the book begins this way, starting with the story of Shmuel's birth and his education and his prophet-hood etc. The rest of the book, which deals with the events relating to Shaul and David, can also be attributed to Shmuel, since Shaul and David are "his doing", in that he found them and anointed them as kings. In this respect, the entire sefer is about Shmuel, and thus rightly named.
- The transition from the period of judges (shoftim) to the period of kings (melachim). Shmuel was the last of the judges and David was the first of the kings (discounting Shaul). Arguably, each of these personalities was the greatest of their respective categories, and so this can also be looked at as the high point of both periods. We would then describe this sefer as the story of lives of Shmuel and David, which marked a turning point in Jewish leadership. Of course, this necessitates the stories of Eli and Shaul to be included as well, given their importance to the Shmuel and David narratives. Now, we cannot call the book by two names (Shmuel and David), and so we choose Shmuel because he was the greater of the two with respect to his level of prophecy and with respect to his parentage, and because he was David's teacher and deserving of his respect.
