Zaccai, Zaccheus, and Remembering

Zaccai’s descendants, 760.
-Ezra 2:9

Zaccai means, "remembered by God", and, "purified for the Lord".

What does, "God remembered" mean?

God remembered Noah, as well as all the wildlife and all the livestock that were with him in the ark. God caused a wind to pass over the earth, and the water began to subside. (1)

And God heard their groaning; and God remembered his covenant with Abraham, with Isaac, and with Jacob; (2)

The next morning Elkanah and Hannah got up early to worship before the Lord. Afterward, they returned home to Ramah. Then Elkanah was intimate with his wife Hannah, and the Lord remembered her. (3)
 -Genesis 8:1, Exodus 2:24, and 1 Sam. 1:19

NET notes:

1. The Hebrew word translated “remembered” often carries the sense of acting in accordance with what is remembered, i.e., fulfilling covenant promises (see B. S. Childs, Memory and Tradition in Israel [SBT], especially p. 34).
2. The verb זָכַר (zakhar, “to remember”) means to begin to act on the basis of what is remembered. A prayer to God that says, “Remember me,” is asking for more than mere recollection (see B. S. Childs, Memory and Tradition in Israel [SBT], 1-8). 
3. The verbs זָכַר (zakar) is often translated “remember.” It does not simply mean the ability to recall (as “forgetting” does not simply mean the inability to recall). It means the decision to recall or to bear in mind, here with regard to her previous request. The Hebrew verb is often used in the OT for considering the needs or desires of people with favor and kindness.

Do names matter?
Do names have significance?
What would it mean if you are part of that tribe?

The name Zaccai in the Bible
There's probably only one man named Zaccai in the Bible, although it seems plausible that the name Zaccheus is the Hellenized version of this name. Both Ezra and Nehemiah mention him as the patriarch of 760 regular people (not priests) who returned from the Babylonian exile (Ezra 2:9, Nehemiah 7:14).
The Masoretes believed that the Zabbai mentioned in Nehemiah 3:20 wasn't really called Zabbai but rather Zaccai, but of the modern English translations only the JSP follows that suggestion. The rest of the versions read Zabbai here.

 Luke 19:1-9
He entered Jericho and was passing through. There was a man named Zacchaeus who was a chief tax collector, and he was rich. He was trying to see who Jesus was, but he was not able because of the crowd, since he was a short man. So running ahead, he climbed up a sycamore tree to see Jesus, since he was about to pass that way. When Jesus came to the place, he looked up and said to him, “Zacchaeus, hurry and come down because today it is necessary for me to stay at your house.” 
So he quickly came down and welcomed him joyfully. All who saw it began to complain, “He’s gone to stay with a sinful man.”
 But Zacchaeus stood there and said to the Lord, “Look, I’ll give half of my possessions to the poor, Lord. And if I have extorted anything from anyone, I’ll pay back four times as much.”
“Today salvation has come to this house,” Jesus told him, “because he too is a son of Abraham. 

By Niels Larsen Stevns - Own work (photo: Gunnar Bach Pedersen) (Randers Museum of Art, Randers, Denmark), Public Domain,