Our Gemara on amud aleph discusses a teaching of Rabbi Yitschok Migdla’ah:

שְׁלֹשָׁה מַטְבְּעוֹת זֶה עַל גַּב זֶה. אָמַר רַבִּי יִצְחָק מַגְדְּלָאָה: וְהוּא שֶׁעֲשׂוּיִין כְּמִגְדָּלִין. תַּנְיָא נָמֵי הָכִי: מָצָא מָעוֹת מְפוּזָּרוֹת – הֲרֵי אֵלּוּ שֶׁלּוֹ, עֲשׂוּיִין כְּמִגְדָּלִים – חַיָּיב לְהַכְרִיז. וְאֵלּוּ הֵן עֲשׂוּיִין כְּמִגְדָּלִים? שְׁלֹשָׁה מַטְבְּעִין זֶה עַל גַּב זֶה.

The mishna teaches: And for these found items, one is obligated to proclaim his find: Three coins stacked one atop another. Rabbi Yitzḥak from Migdal says: And one is obligated to proclaim the find in a case where the coins are arranged in well-ordered towers. This is also taught in a baraisa: If one found scattered coins, these belong to him. If the coins are arranged in well-ordered towers, he is obligated to proclaim his find. The baraisa elaborates: And these coins are arranged in towers: Three coins stacked one atop another.

This is a remarkable coincidence. The rabbi’s name (Migdla’ah) also corresponds with the subject matter of the teaching (a pile of coins, in Hebrew, Migdal.)

Maharitz Chayes here notes that this is a practice of the Gemara to name various Amoraim after their teachings. Perhaps this is like the way we call great authors by the name of their works, such as the Chofetz Chaim.  There truly is a fascinating list of these correspondences between names of the rabbis and teachings.  (Also see Rav Margulies’ Sefer, “Le-Cheker Shemos Batalmud”.) I will list just a few of the most striking cases:

• Chulin (30b) a Rabbi Yonah is discussing a legal case of a Yonah bird slaughtered by a hunters arrow.
• Berachos 53b, where a Rav Zehumai discusses the halachic implications when one’s hands are dirty (The Aramaic word for filth is Zuhama.)
• Bava Metzia 55a Rav Ketina says: The court attends to monetary claims of even less than the value of one peruta. Katina means small, and the Rav Katina is allowing even for small monetary claims

There are many more examples.  The question is, why?  Mahariyz Chayes seems to hold that it was to honor the person by naming them after their teaching. I would add, it may be that their name was similar, and so a mnemonic to aid memory and as an honor, they played the person’s name after the teaching.  This also must be the case with some otherwise horrendous Biblical names.  Which Jewish mother names their child, “Machlon and Kilyon”, which means, “illness and destruction”? Obviously, Megillas Rus is making a pun that their names correspond to their fates.  But they must have had names similar to this, such as Menachem and Kala, or whatever. (A similar comment is made by Rav Yosef Bechor Shor (Bereishis 38:7) in regard to Yehuda’s son, Er, which spelled backwards is Ra (evil), as he committed evil in the eyes of God (ibid 38:10.)

I also think there might be an added dimension. In Jewish thinking, a name is an essence. This is why Yaakov wants to know the name of the angel he wrestles with (32:30) so he can grasp the angel’s essence and somehow master it.  Likewise, the whole idea of the Avrohom, Sarah and Yaakov having their names change to signify a change of fate also speaks to this. 

In Pirke Avos, sometimes a teaching of a sage is introduced as, “Hu Haya Omer” “He would say.”  It has the implication that he often said this (see Magen Avos 1:2), feeling it was a key teaching.  As a child, I heard from my father Z”L in the name of someone I do not remember (perhaps Rav Hutner ZT’L), that it is deeper than that. “Hu” “HE” would say, that is, his essence said it.  This might be similar to what we discussed in Psychology of the Daf Bava Kama 114, that Rabbi Yehuda Hanasi would introduce some of his teachings with the phrase, ‘Omer ani”, which translates roughly as “I say”, but in Hebrew it might have a deeper connotation. Rav Yosef Engel (Beis Haotzar, Ma’areches aleph-vav, klal 33) notes that the meaning is something like “my essence dictates”, that is Rabbi Yehuda Hanasi felt a deep truth coming from within, an indication of the will of God channeled from his soul.  

Thus, these rabbis did not coincidentally have names that corresponded with their teachings, but rather, their names and their teachings and their essence were one in the same! (Possibly when their names were homophonic with the teaching, such as maybe Rav Midgla’ah’s real name was Gedaliah, the rabbis felt it was not a coincidence. His essence from his name came out in his pursuit and understanding of Torah.

Megaleh Amukos (Va'eschanan 186:1) writes that the soul of every Jew stems from one of the 600,000 letters in the Torah. The Torah Speaks Through Us, and in Fact, is Us.  Yisrael, V’eoraysa, V’Kudsha Brich Hu - Chad Hu (Peri Tzaddik, Terumah 4).

Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation

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