Abba bar Abba the Kohen, the father of Shmuel, is called the father of Shmuel due to an incident brought in the Talmud (Gittin 5a). Abba bar Abba went to the West and encountered a woman who knew the language of Tzipori. She said to him, "I have a need, and I will give you such and such coins," because she knew that a great man would emerge from him. He left her and came that night to his wife, and he had relations with her, and afterwards it was heard that she was pregnant and brought to the Beit Din to be examined.
Shmuel said, "In the womb of his mother, let him be like the head of a fool, lest I receive the head of a fool and it will pain me." The head of a fool in the womb of his mother and the head of a fool is removed. [And a bit of this you will see in Tosafot, Kidushin (17a). (It is written in the book Ginat Veradim, section Pei, that this incident was the reincarnation of Potiphar's wife who accused Yosef, for she knew that from him would emerge a great man.) And it is written in the book Ginat Veradim, section Aleph, that it is difficult why he is called after his son. The matter is that Abba bar Abba is Shmuel the Ramathi, and Shmuel his son is the reincarnation of Shaul, and just as Shmuel spoke with Shaul after his death, so Abba bar Abba spoke with his son Shmuel after his death, as it is stated in Berakhot (18b).
And just as the woman (the Ba'alat Ov) said, "Whom shall I bring up for you?" they also said to him, "There are many here, father," and just as Shmuel said to Shaul, "Tomorrow you and your sons will be with me," so Abba bar Abba said to Shmuel his son, "You are coming to the calf." And just as he said to Shaul, "With me in my company," so Abba bar Abba said to Shmuel, "You are considered greatly in this world." And Shmuel is a reincarnation and a spark of King Shaul, for Shmuel is called "Arioch, king of the law," as Shmuel is in judgment. (And a hint to this is that Arioch, king, with the letters and two inclusives, totals the number of Shaul.) And my master, my father, wrote in his work that Shmuel the Ramathi was from the side of the female, therefore Hannah said, "And you will give your maidservant a seed of men," attributing it to his mother (Maggid, Ophan 100). And because Abba bar Abba is Shmuel the Ramathi, therefore he is called Abba bar Abba, meaning that he is not dependent on his mother but on his father, for he is not from the side of the female. [That is to say, not like Abba, who is Shmuel the Ramathi, who was from the side of the female, but this Shmuel is dependent on his father, therefore he is called Abba bar Abba Shmuel.] And my master wrote, and to this secret Hannah said, "I am the one who asked for him," a spark of the Holy Spirit because Shmuel is the son of his father Shaul.
And see Yalkut Shmuel, section Pei.]
Seder_HaDorot,_Tanaim_and_Amoraim.2:1