Everyone here has a write-up, drawn from the same records that explain the names while you read the text.
Cyrus
King of PersiaThe Persian king whose policy was to send captive peoples home with their gods and their temple goods. For Judah that meant the end of exile. Isaiah names him as the LORD's shepherd and anointed, and a clay cylinder in the British Museum records his general policy in his own words.
Isaiah 44:28-45:1Ezra 1:1-4
Ezra
Priest and scribeA scribe who set his heart to study the law, to do it, and to teach it. He led a second group of exiles home and read the law aloud to the assembled people, with others explaining it so everyone could understand.
Ezra 7Nehemiah 8
Eleazar
Aaron's surviving sonsAaron's third and fourth sons, who inherited the priesthood after the older two, Nadab and Abihu, were killed offering unauthorized fire. Eleazar succeeded Aaron as high priest and stood with Joshua to divide the land.
Exodus 6:23-25Leviticus 10:1-7Numbers 20:25-28
Parosh
The families that came backThe register of those who returned from Babylon, given twice at length in Ezra 2 and Nehemiah 7 and a third time in 1 Esdras. Roughly fifty thousand people, listed by family, by town, and by temple office.
Ezra 2:1-70Ezra 8:1-20Nehemiah 7:6-73
Shishak
Foreign kings and their officersThe rulers outside Israel who invade, extract tribute, or grant permission. Shishak of Egypt stripped the temple in Rehoboam's fifth year and left a relief at Karnak listing the towns he took. Necho killed Josiah at Megiddo. Tiglath-pileser III began the Assyrian deportations.
Genesis 14:1-171 Kings 14:25-262 Kings 15:29
Libni
The Levite clan headsThe sons and grandsons of Levi's three houses, named in the genealogies that open Exodus 6 and Numbers 3 and fill the Chronicler's registers. Libni and Shimei from Gershon; Amram, Izhar, Hebron, and Uzziel from Kohath; Mahli and Mushi from Merari.
Exodus 6:14-25Numbers 3:17-351 Chronicles 6:1-30
Zerubbabel
Leaders of the returnThe governor and the high priest who led the first returning exiles, laid the foundation of the second temple, and finished it under the preaching of Haggai and Zechariah.
Ezra 3:8-13Ezra 5:1-2Haggai 2:20-23
Meshullam
Names of the priestly housesNames that recur constantly through Chronicles, Ezra, and Nehemiah, often carried by several different men, and usually attached to the priestly and Levitical families. They are among the most common Hebrew names of the period, which is why the text so often has to add a father's name to tell them apart.
1 Kings 12:22-24Ezra 2:59-63Ezra 8:15-20