Another interpretation: the term "Jered" denotes nothing but kingship, as you say, "May he have dominion from sea to sea" (Psalms 72:8), and it is written, "For he had dominion over all the region beyond the River" (1 Kings 5:4). "The father of Gedor" (1 Chronicles 4:18) - many who built fences [protectors] arose for Israel, and this one was the father of them all. "Heber" - because he joined [hibber] the children to their Father in heaven.
Moses as King and the One Who Bound Children to Their Father in Heaven
Yalkut Shimoni on Torah 428:4
דָּבָר אַחֵר אֵין לְשׁוֹן יֶרֶד אֶלָּא לְשׁוֹן מַלְכוּת, כְּמָה דְּאַתְּ אָמַרְתְּ (תהלים עב, ח) "וְיֵרְדְּ מִיָּם עַד יָם", וּכְתִיב (מלכים א ה, ד) "כִּי הוּא רֹדֶה בְּכָל עֵבֶר הַנָּהָר" (דברי הימים שם) "אֲבִי גְדוֹר", הַרְבֵּה גּוֹדְרִין עָמְדוּ לְיִשְׂרָאֵל, וְזֶה הָיָה אֲבִיהֶן שֶׁל כֻּלָּן "חֶבֶר" שֶׁחִבֵּר הַבָּנִים לַאֲבִיהֶן שֶׁבַּשָּׁמַיִם.