Batei midrash of other sages are in fact mentioned, they're just usually referred to in Aramaic "בי" - "Bei".
Bei Rabbi Yannai:
"דְּבֵי רַבִּי יַנַּאי אָמְרִי, מֵהָכָא: ״וְדִי זָהָב״.
The Sages of the school of Rabbi Yannai, however, say proof that Moses spoke impertinently toward God on High is derived from here, Moses’ rebuke at the beginning of Deuteronomy: “And Di Zahav” (Deuteronomy 1:1). (for more, see here)
From a quick search, I also found one mention of the title of his beit midrash in Hebrew:
"בית רבי ינאי הוון מכילין בה דבש. The Sages of the school of Rabbi Yannai would measure in it honey." (Yerushalmi Shabbat 54b)
Bei Rabbi Eliezer ben Yaakov:
"שֶׁכֵּן דְּבֵי רַבִּי אֱלִיעֶזֶר בֶּן יַעֲקֹב קוֹרִין לָאַלְפִין עַיְינִין, וְלָעַיְינִין אַלְפִין.
The Gemara explains the basis for this interpretation: As the Sages of the school of Rabbi Eliezer ben Ya’akov would indiscriminately read alef as ayin and ayin as alef and in this case transforming el into al. (for more, see here)
Bei Rabbi Sheila:
"וְיֹאשִׁיָּה גּוּפֵיהּ הֵיכִי שָׁבֵיק יִרְמְיָה וּמְשַׁדַּר לְגַבַּהּ אָמְרִי דְּבֵי רַבִּי שֵׁילָא מִפְּנֵי שֶׁהַנָּשִׁים רַחֲמָנִיּוֹת הֵן
The Gemara asks: But how could Josiah himself ignore Jeremiah and send emissaries to Huldah? The Sages of the school of Rabbi Sheila say: Because women are more compassionate, and he hoped that what she would tell them would not be overly harsh." (for more, see here)
Bei Rabbi Yishmael:
"דְּבֵי רַבִּי יִשְׁמָעֵאל: ״וּכְפַטִּישׁ יְפֹצֵץ סָלַע״, מָה פַּטִּישׁ זֶה נֶחֱלָק לְכַמָּה נִיצוֹצוֹת — אַף כׇּל דִּיבּוּר וְדִיבּוּר שֶׁיָּצָא מִפִּי הַקָּדוֹשׁ בָּרוּךְ הוּא נֶחֱלַק לְשִׁבְעִים לְשׁוֹנוֹת. And, similarly, the school of Rabbi Yishmael taught with regard to the verse: “Behold, is My word not like fire, declares the Lord, and like a hammer that shatters a rock?” (Jeremiah 23:29). Just as this hammer breaks a stone into several fragments, so too, each and every utterance that emerged from the mouth of the Holy One, Blessed be He, divided into seventy languages." (for more, see here)
"אביי אומר אתיא מדתני דבי חזקיה דתנא דבי חזקיה (שמות כא, כד) עין תחת עין נפש תחת נפש ולא נפש ועין תחת עין ואי סלקא דעתך ממש זימנין דמשכחת לה עין ונפש תחת עין דבהדי דעויר ליה נפקא ליה נשמתיה
The Gemara presents another derivation: Abaye says that this principle is derived from that which was taught by the school of Ḥizkiyya, as the school of Ḥizkiyya taught that the Torah states: “An eye for an eye” (Exodus 21:24), and: “A life for a life” (Exodus 21:23), but not an eye and a life for an eye. And if it enters your mind to say that the verse means this literally, there could be times when you find a case where both an eye and a life are taken for an eye, i.e., when the one who caused the damage is so weak that as the court blinds his eye, his soul departs from his body." (for more, see here)
And so forth.