List of people / positions, by Sefaria statement.
Tanna Kamma - anonymous. Discusses terminus ad quo of recitation. Exists as a separate entity from Rabbi Eliezer who discusses the terminus ad quem, assuming that the punctuation with period is correct. (See gemara's discussion.) Since discusses similar concept to that
רַבִּי אֱלִיעֶזֶר = Rabbi Eliezer ben Hyrcanus. Tanna generation 3. Shammaite.
וַחֲכָמִים = Anonymous plural Sages, disagreeing with Rabbi Eliezer. These Sages should be contemporary to Rabbi Eliezer, as a disputant. Also, the contemporary Rabban Gamliel is about to discuss their position, so they should be in the present or in previous generations to Tanna generation 3.
רַבָּן גַּמְלִיאֵל = Rabban Gamliel II. Tanna generation 3. It is not Rabban Gamliel I (HaZaken) because that is too early, nor Rabban Gamliel III (the son of Rabbi Yehuda HaNasi), of the transitional Tanna / Amora generation, as that is not contemporary with Rabbi Eliezer, nor is likely to be included in the Mishnah. The other two, IV and IV, are Amoraim and not in scope at all. This Rabban Gamliel II is Rabbi Eliezer's brother-in-law, having married Rabbi Eliezer's sister. He was appointed Nasi in 80 CE and died approximately 114 CE.
בָנָיו = Rabban Gamliel's sons, in the plural. Of his children, a Jewish Encyclopedia article (authored by Solomon Schechter, Wilhelm Bacher) asserts that he had a daughter, "who answered in a very intelligent fashion two questions addressed to her father by an unbeliever (Sanh. 34a, 90b)." Examining those Talmudic passages, Rashi asserts that this was the daughter of the Roman emperor, who was Rabban Gamliel's interlocutor, rather than Rabban Gamliel's daughter. The same article asserts that "Two of Gamaliel's sons are mentioned as returning from a certain feast (Ber. i. 2)." The implication is that there may be several more. This reference is to our present passage, but the claim that these are specifically two, and not more, is unsupported by the text. The minimum of plural is two, but not the maximum. They suggest Rabban Shimon ben Gamliel II (who was Rabbi Yehuda HaNasi's father) and Rabbi Yehuda ben Gamliel. These spanned several generation, including the generation of Rabbi Meir (fifth generation Tanna).
אָמְרוּ לוֹ = this and other explicit and implicit pronouns throughout. Since the conversation is with his mature sons, the conversation occurs in the overlap between generations,
חֲכָמִים = This statement was either voiced by the Mishnah or by Rabbi Eliezer. It should refer to the same group of Sages as before, namely Rabbi Eliezer's disputants.
חֲכָמִים = the same
Commentary: Shema is not tied specifically to korbanot or to established prayers by the Avot, but to a Biblical command. Still, as prayers took the place of the korbanot we could no longer offer, perhaps the concern in establishing these fixed times is expressed well by these early Tannaim who were just post-destruction.
6, 8, 11
תַּנָּא = the anonymous author of the Mishna who frames the question.