Probably from the same as 'eythan (in the sense of patience); a female donkey (from its docility) -- (she) ass.
see HEBREW 'eythan
H860. athon
אָתוֺן noun feminineGenesis 45:23 she-ass (Arabic , Aramaic אַתָּנָא, , Assyrian atânu) — אָתוֺן Numbers 22:23 10t.; אֲתֹנְךָ 22:30, 32; אֲתֹנוֺ Genesis 49:11 2t.; plural absolute אֲתֹנֹת 12:16 2t.; אֲתֹנוֺת Judges 5:10 12t.; אֲתוֺנוֺת Job 1:3; 42:12; — she-ass, as dam Genesis 49:11; Zechariah 9:9; as property (constituting wealth) Genesis 12:16; 32:16; Job 1:3, 14; 42:12 compare 1 Chronicles 27:30; so of the asses of Kish 8 t. 1 Samuel 9:3 (twice in verse); 9:5, 20; 10:2 (twice in verse); 10:14, 16; as beasts of burden Genesis 45:23; for riding Judges 5:10; Numbers 22:21-22, 2 Kings 4:22, 24; of Balaam's ass 14 t. Numbers 22:21-22, 23 (3 t. in verse); 22:25, 27 (twice in verse); 22:28-29, 30 (twice in verse); 22:32-33,.
אַתֵּנָה אַתֵּן, see below אנת.
אֶתְנָה see תנה.