The OP's question presumes that primarily only the tribe of Judah/Yehuda endured, which is why we are called Jews today.
My answer attempts to show the fallacy of such a presumption.
First, it's important to note that the Talmud (Bava Basra 115b) posits in the name of Abaye, that גמירי דלא כלא שבטא, we have a tradition that no tribe will ever be entirely destroyed.
Rashbam (ad loc.) cites Rabbeinu Chananel, who brought support to this axiom from the verse in Malachi (3:6) כִּ֛י אֲנִ֥י יְהֹוָ֖ה לֹ֣א שָׁנִ֑יתִי וְאַתֶּ֥ם בְּנֵֽי־יַעֲקֹ֖ב לֹ֥א כְלִיתֶֽם, "For I, the Lord, have not changed; and you, the sons of Jacob, were not destroyed".
So while we may not know our individual lineages, we still know, traditionally, that among us, are members of ALL the different tribes.
I note, that that in most of the Bible, the Hebrews are referred to as Israel, or the Children of Israel (not Hebrews). At some point, probably near the time of the Babylonian exile, they are started to be referred to as "Yehudim" (Judah-im) (Jews). This is indicated in the Book of Esther, which is replete with the term.
It would be pure sophistry to suggest that the Book of Esther is only about the tribe of Judah, which was endangered by the evil decree of Ahasuerus and Haman, while all the other tribes of Israel were unaffected by the decree.
This is also indicated in the verse (Esther 3:6) "And it was contemptible in his eyes to lay his hands on Mordecai alone, for they had told him Mordecai's nationality" (not tribe).
I also note the verse in Jeremiah (34:9)
לְ֠שַׁלַּח אִ֣ישׁ אֶת־עַבְדּ֞וֹ וְאִ֧ישׁ אֶת־שִׁפְחָת֛וֹ הָֽעִבְרִ֥י
וְהָֽעִבְרִיָּ֖ה חָפְשִׁ֑ים לְבִלְתִּ֧י עֲבָד־בָּ֛ם בִּיהוּדִ֥י
"That every man should set his manservant, and every man his
maidservant, the Hebrew male and Hebrew female, free, that
none should hold his Jewish ("Yehudi") brother as a slave.
This seems to indicate, that all children of Israel are referred to as "Yehudim".
The Talmud (Megillah 13a) states that the word Jew is synonymous with those deny idolatry, hence this refers to all Yehudim.