The source given there, Otzar Midrashim, is an anthology of midrashic works from different periods. In this case, the information comes from a work entitled Divrei ha-Yamim le-Moshe Rabbeinu, which is of unknown date and authorship, but at any rate predates the Aruch (11th century - beginning of the era of the Rishonim), which quotes this etymology (under s.v. אהרן). [Among other Rishonim, Ibn Ezra (to Ex. 2:22 and 4:20) mentions it but dismisses it as a reliable source; Rashbam to Ex. 4:9 refers to it obliquely (as "ספרים החיצוניים") and likewise rejects the story told there about Moshe's speech defect, though to Num. 12:1 (thanks to jake for this reference) he accepts the story from there about Moshe's rule in Cush; and Yalkut Shimoni uses material from it without reservation.]
Kabbalistically, Seder Hadoros quotes a couple of sources who associate the name אהרן with הרן (Avraham's brother), and say that Haran's soul was reincarnated in Aharon.