The name Esau in the Bible
Esau is mentioned three times in the Greek New Testament (spelled Ηασυ): Romans 9:13, Hebrews 11:20 and 12:16.
Etymology of the name Esau
The two nicknames of Esau, Edom and Seir, are both obvious in meaning and have to do with Esau's looks (red and hairy). His proper name however is not as easily derived.
Jones' Dictionary of Old Testament Proper Names reports that there once was a root עשה ('asa) that meant to be hairy, and refers to an existing Arabic verb that means just that. Hence Jones translates with Covered With Hair, and the NOBSE Study Bible Name List reads Hairy.
However, the regular Hebrew word for hair in the Bible is שער (s'r)—this noun also yields the name Seir—and a Hebrew audience would probably have a much stronger association to the very common Hebrew verb עשה ('asa), meaning to do or accomplish:
The twins Jacob and Esau have appealed to the imagination of Biblical exegetes since forever. Augustine of Hippo for instance thought that Jacob represented the saved and Esau the lost.
Since Esau is also called Edom (meaning Dustling or Corporeal One), perhaps these twins reminded Isaac and Rebekah of the basic workings of a human individual: the animal body, though wonderfully made (Psalm 139:14) should be subjected to the grace filled mind (Romans 8:10).
And although the body does all the work, the higher mind takes all the credit (Romans 6:12; also see 1 Corinthians 6:19 and Matthew 23:16-17).
To a Hebrew audience the name Esau means Doer.