In the sense of “noble origin” the word is not in the Quran: aṣīl and its plural āṣāl there mean only the end of the day, as in “And glorify Him morning and evening (bukratan wa asila)” (33:42). The sense of “good stock” goes back to asl, the root of a tree, in the parable of the good word, “whose root is firm and whose branches are in the sky” (14:24).
Meaning of the name Aseel
Asil (aṣīl) comes from aṣl, “root, origin” (root ʾ-ṣ-l): something with firm roots, a man of good stock, a purebred horse, a sound and genuine opinion. The same word also means late afternoon. The girls’ name Asil (أسيل, with a plain s), very popular in the Arab world and usually spelt Aseel, is a different word: it describes a smooth, soft and long cheek, a mark of beauty for the poets. In Turkey, Asil (“noble”) is a common boys’ name.
Have you not considered how Allāh presents an example, [making] a good word like a good tree, whose root is firmly fixed and its branches [high] in the sky?