🔼The name Aaron in the Bible
The name Aaron (spelled Ααρων in the New Testament) is unique in the Bible, and is applied only to Aaron the Levite, brother of Moses and Miriam. Aaron was the first high priest of Israel (Exodus 28:1) and his descendants filled a sub-caste within the priestly caste of Israel (Joshua 21:4).
🔼Etymology of the name Aaron
The name Aaron is not a regular Hebrew word and that's possibly because it originated elsewhere (probably Egypt). But since most names in the Bible mean something and foreign names often were transliterated into Hebrew in such a way that they began to mean something in Hebrew, it's interesting to see what the name Aaron may have meant to a Hebrew audience.
Jones' Dictionary of Old Testament Proper Names derives Aaron from the Hebrew word הר (har) meaning mountain, hill (and a mountain is sometimes used as metaphor for a large group of people). From this perspective, the name Aaron is related to the Hebrew names Ararat and Haran.
Another way of looking at the name Aaron (as does NOBSE Study Bible Name List) is to follow the Hebrew root אור ('or) meaning to be or become light:
There may even be relations between the name Aaron and the word ארון ('aron), meaning chest or Ark (see the name Aran). This word is used for an offer chest (2 Kings 12:10), a sarcophagus (Genesis 50:26) but mostly to indicate the Ark of the Covenant (Exodus 25:10).
And finally we note the curious similarity between the name אהרן (Aaron; spelled with the letter ה) and the adjective אחרון (aharon; spelled with the letter ח), meaning hindermost, latter or last. See any of the אחר-names (like Aharah) for more details on this word.
For a meaning of the name Aaron, NOBSE Study Bible Name List reads Bright. Jones' Dictionary of Old Testament Proper Names reads Very High.