Abdi means my servant. It is the name of three different men in the Bible. Each one is mentioned only one time.  

1. He was the grandfather of a certain Ethan who was a Levite of the family of Merari (1Chronicles 6:44And their brethren the sons of Merari stood on the left hand: Ethan the son of Kishi, the son of Abdi, the son of Malluch,
   See All...) and who served in the time of David as one of the singers for the worship of God (1Chronicles 6:31-32 [31] And these are they whom David set over the service of song in the house of the LORD, after that the ark had rest. [32] And they ministered before the dwelling place of the tabernacle of the congregation with singing, until Solomon had built the house of the LORD in Jerusalem: and then they waited on their office according to their order.
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2. He was the father of Kish who was a Levite in the days of King Hezekiah (2Chronicles 29:12Then the Levites arose, Mahath the son of Amasai, and Joel the son of Azariah, of the sons of the Kohathites: and of the sons of Merari, Kish the son of Abdi, and Azariah the son of Jehalelel: and of the Gershonites; Joah the son of Zimmah, and Eden the son of Joah:
   See All...) and who helped in 727BC [Reese] in the first year of Hezekiah’s reign (2Chronicles 29:3He in the first year of his reign, in the first month, opened the doors of the house of the LORD, and repaired them.
   See All...) to cleanse the temple (2Chronicles 29:15-16 [15] And they gathered their brethren, and sanctified themselves, and came, according to the commandment of the king, by the words of the LORD, to cleanse the house of the LORD. [16] And the priests went into the inner part of the house of the LORD, to cleanse it, and brought out all the uncleanness that they found in the temple of the LORD into the court of the house of the LORD. And the Levites took it, to carry it out abroad into the brook Kidron.
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He is listed as one of the sons of Elam (Ezra 10:26And of the sons of Elam; Mattaniah, Zechariah, and Jehiel, and Abdi, and Jeremoth, and Eliah.
See All...) who separated from their “strange wives” (that is, they divorced their Gentile wives) in obedience to the command of Ezra (Ezra 10:10-11 [10] And Ezra the priest stood up, and said unto them, Ye have transgressed, and have taken strange wives, to increase the trespass of Israel. [11] Now therefore make confession unto the LORD God of your fathers, and do his pleasure: and separate yourselves from the people of the land, and from the strange wives.
See All...) in 457BC [Reese].