וְנָתַ֤ן מַלְכֵיהֶם֙ בְּיָדֶ֔ךָ וְהַאֲבַדְתָּ֣ אֶת־שְׁמָ֔ם מִתַּ֖חַת הַשָּׁמָ֑יִם לֹֽא־יִתְיַצֵּ֥ב אִישׁ֙ בְּפָנֶ֔יךָ עַ֥ד הִשְׁמִֽדְךָ֖ אֹתָֽם׃
און ער װעט געבן זײערע מלכים אין דײַן האַנט, און װעסט אונטערברענגען זײער נאָמען פֿון אונטערן הימל; קײנער װעט ניט באַשטײן פֿאַר דיר, ביז דו װעסט זײ פֿאַרטיליקן.
Ibn Ezra
Your annihilating is a verbal noun; even though the second syllable is vocalized with a ḥiriq , the phrase “leaving [Hebrew: hish כ ir] him a survivor” [Numbers 21: 35] exhibits a (probably) similar construction. Conclusive evidence here is them, the direct object of the verb.
Or HaChaim
ונתן מלכיהם בידך, "He will deliver their kings into your hand, etc." You will capture them alive. We have proof of this in Joshua 10,26.
Sforno
ונתן מלכיהם בידך והאבדת את שמם, for allowing any of these Canaanites to survive would become an ongoing source of irritation for you, as demonstrated by the young Haddad, sole survivor of the people of Edom, who became a lifelong source of irritation (militarily) for such a powerful king as Solomon. (Kings I 11,14 and onwards)