Genesis 19:37–38 (JPS):
וַתֵּלֶד הַבְּכִירָה בֵּן וַתִּקְרָא שְׁמוֹ מוֹאָב הוּא אֲבִי מוֹאָב עַד הַיּוֹם. וְהַצְּעִירָה גַם הִוא יָלְדָה בֵּן וַתִּקְרָא שְׁמוֹ בֶּן עַמִּי הוּא אֲבִי בְנֵי עַמּוֹן עַד הַיּוֹם. / And the first-born bore a son, and called his name Moab—the same is the father of the Moabites unto this day. And the younger, she also bore a son, and called his name Ben-ammi—the same is the father of the children of Ammon unto this day.
Judges 10:6 (JPS):
…וְאֶת אֱלֹהֵי אֲרָם וְאֶת אֱלֹהֵי צִידוֹן וְאֵת אֱלֹהֵי מוֹאָב וְאֵת אֱלֹהֵי בְנֵי עַמּוֹן וְאֵת אֱלֹהֵי פְלִשְׁתִּים…. / …and the gods of Aram, and the gods of Zidon, and the gods of Moab, and the gods of the children of Ammon, and the gods of the Philistines….
Ⅰ Chronicles 18:11 (JPS):
…מֵאֱדוֹם וּמִמּוֹאָב וּמִבְּנֵי עַמּוֹן וּמִפְּלִשְׁתִּים וּמֵעֲמָלֵק. / …from Edom, and from Moab, and from the children of Ammon, and from the Philistines, and from Amalek.
In fact, almost every time Amon is mentioned in Tanach, it's called "בְּנֵי עַמּוֹן", "the children of Amon", unlike other nations. Why is it?
(Perhaps the name of the nation is actually "בְּנֵי עַמּוֹן", "B'ne Amon", (and the demonym "Amoni" would be like "Y'mini" for a Benjaminite,) perhaps named after בֶּן עַמִּי. However, arguing against that is the fact that "Amon" is occasionally used alone: e.g., Ⅰ Samuel 11:11 and Psalms 83:8.)