Ahitub - brother of goodness = good. A few people in the Bible have this name:
(1.) The son of Phinehas, grandson of Eli, and brother of Ichabod. On the death of his grandfather Eli he most likely succeeded to the office of high priest, and would have been succeeded by his son Ahijah (references to Ahitub as the father of are in 1 Sam. 14:3; 22:9, 11, 12, 20). Ahijah (also spelled Ahiah), who is listed as his son in 1 Samuel 14:2-3, 18-19, may have been the same person as Ahimelech (1 Samuel 22:9-20), or he may have been another son of Ahitub (probably an elder son if this was the case).
(2.) The father of Zadok (2 Sam. 8:15-17). This Ahitub was the son of Amariah, who was the son of Meraioth, who was the son of Zerahiah, who was the son of Uzzi, who was the son of Bukki, who was the son of Abishua, who was the son of Phinehas, who was the son of Eleazar, who was the son of Aaron (1 Chronicles 6:3-8). There is a faint possibility that this Ahitub was made high priest by Saul after the extermination of the family of Ahimelech, but it is very unlikely as there are apparently no references supporting this. It is much more likely that Saul had no official high priest after this incident until the end of his reign (see Josephus's Antiquities of the Jews, Book VI, Chapter XII, Paragraph 7
(3.) A priestly descendant through the priestly line of the first Zadok. This Ahitub is mentioned in 1 Chronicles 6:11-12 To make matters a bit more confusing, this Ahitub also had a son (or probably grandson) by the name of Zadok. This Ahitub may have been high priest in the later time of the kings, but he also may not have been a high priest. He did become the ancestor of later high priests, which served during the fall of Jerusalem and post-exile.
(4.) An ancestor of a person mentioned in Nehemiah 11:11 This person might be one of the three prementioned persons, but probably is not.