Prof. Ephraim Urbach in "Chazal - Pirkei Emunot V'De'ot", pg. 532-533 based this view on the fact that REB"Ch was a student of Beit Shammai and in Sifrei Zuta, Y.N. Epstein edition, it says that there were Idumean students in Beit Shammai, and according to Josephus, Elazar ben Chananyah led a group of Idumean rebels during the Revolt.
Ben Tzion Luria in "Megillat Taanit", pg. 9-10 wrote that Solomon Zeitlin held this view, and brings another possible basis, in that according to Megillat Taanit, its author was R' Elazar ben Chananyah, which suggests that he held zealous views of liberty, much like Elazar ben Chananyah.
Another basis for this may be that Chananyah ben Nedavai, father of Elazar, one of the last High Priests of the Second Temple, is called in the Talmud "Yochanan ben Nedavai/Nerbai/Garbai", and according to Rabbi Dr. Shmuel Klein in his essay "לחקר השמות והכנוים", per the Talmud, is probably a nickname referring to his generosity: He made sure to feed many priests from the remains of the sacrifices and offerings. In the gemara in Pesachim 57a, it says: "They said about Yoḥanan ben Narbbai that he and his household would eat three hundred calves, and drink three hundred jugs of wine, and eat forty se’a of doves for dessert."1 This seems similar to what it says about Chananyah ben Chizkiyah, father of Rabbi Elazar ben Chananyah: "What did he, Ḥananya ben Ḥizkiya, do? They brought him three hundred jugs of oil, for light and food, up to his upper story, and he sat isolated in the upper story and did not move from there until he homiletically interpreted all of those verses in the book of Ezekiel that seemed contradictory, and resolved the contradictions." (Shabbat 13b) If Nedavai/Nervai/Garbai is a nickname rather than his father's name, then it would still be plausible that Chananyah's father was really called Chizkiyah.
Therefore, I was wondering whether there were any Orthodox sources that identify one with the other, or discuss why they are not the same person?
1 According to this, all three variants of the nickname make sense: Nedavai - because he was נדיב, generous. Nervai - as in ריבוי, either because of the plentiness of the offerings in his time or because of the many priests he managed to feed. Garbai - after the hundreds of jugs (גרבים) he and his household consumed.