Concise Bible Dictionary:

This is not a proper name, but the title of Nergal-sharezer (Jer. 39:3, 133And all the princes of the king of Babylon came in, and sat in the middle gate, even Nergal-sharezer, Samgar-nebo, Sarsechim, Rab-saris, Nergal-sharezer, Rab-mag, with all the residue of the princes of the king of Babylon. (Jeremiah 39:3)
13So Nebuzar-adan the captain of the guard sent, and Nebushasban, Rab-saris, and Nergal-sharezer, Rab-mag, and all the king of Babylon's princes; (Jeremiah 39:13)
). It has been supposed by some to signify “chief of the Magi,” and by others, “chief priest.” On the monuments it is given as ruba eniga, which has been interpreted “the glorious prince.” This would be an appropriate title if Nergal-sharezer is the same person who became Neriglissar the king.

Strong’s Dictionary of Hebrew Words:

from 7227 and a foreign word for a Magian; chief Magian; Rab-Mag, a Bab. official
KJV Usage:

Jackson’s Dictionary of Scripture Proper Names:

chief soothsayer: much melting

Potts’ Bible Proper Names:

Chief of the magi:― a Babylonian official, Jer. 39:3. {Princeps magorum}