Many rabbis of the same name served as Nasi or Prince.
Reprinted from The Jewish Religion: A Companion, published by Oxford University Press.
Rabban Gamaliel is the name and title of six holders of the office of Nasi, Prince, in Palestine during the first five centuries CE. The title Rabban, "our master," was used to distinguish the Nasi from other rabbis. The office of Nasi was primarily one of religious authority but the Nasi also played an occasional political role in representing the Jewish community to the Roman authorities.
Since practically all the references to the office are in sources compiled later and are far from being contemporary records, it is difficult to know for certain how the office came about and the precise way in which the affairs of the Nasi were conducted. From the later sources (Talmudic and Midrashic) it appears that the first Nasi was Rabban Johanan ben Zakkai, a disciple of Hillel, after whom Rabban Gamaliel, a grandson of Hillel, served as Nasi; the office then became a hereditary one held by Gamaliel's descendants.
A list of princes until the end of the Mishnaic period, that is, until the beginning of the third century CE, can now be given:
1. Rabban Gamaliel the Elder (Gamaliel I), first half of the first century.
2. Rabban Simeon ben Gamaliel (Simeon ben Gamaliel I), son of (1).
3. Rabban Gamaliel of Yabneh (Gamaliel II), son of (2).
4. Rabban Simeon ben Gamaliel (Simeon ben Gamaliel II), son of (3).
5. Rabbi Judah the Prince, editor of the Mishnah, son of (4).
6. Rabban Gamaliel (Gamaliel III) son of (5).
The other three Gamaliels are referred to only very infrequently. Gamaliel VI died in 426 CE, after which the office of Nasi was abolished.
Granted that, as above, the majority of the sources are late, there are echoes in these sources of a degree of conflict between the Nasi, the representative of the establishment, and certain other scholars. According to the Mishnah (Rosh Hashanah 2:8-9), in a dispute between Rabban Gamaliel II and Rabbi Joshua regarding the exact date of Yom Kippur, Gamaliel ordered Joshua to appear before him on "his" Yom Kippur carrying his stick and his money-bag so as to establish the Nasi's authority. According to a Talmudic account (Berakhot 27b-28a), after further humiliations of Rabbi Joshua by Rabban Gamaliel, the latter was deposed, for a time, from the office of Nasi.
In another Talmudic account (Horayot 13b) Rabban Simeon ben Gamaliel II had a dispute with Rabbi Meir and Rabbi Nathan, resulting in the exclusion of these two teachers from participation in the debates in the House of Learning.
In the first chapter of Ethics of the Fathers and in the beginning of chapter 2, a list of sayings of the various Princes is given from Gamaliel I to Gamaliel III but no saying at all of Gamaliel II is quoted. This may be because of Gamaliel II's deposition but it is more likely that sayings of this teacher were originally in the list and were simply slipped out by accident.