🔼The name Meshillemith in the Bible
There is only one man named Meshillemith in the Bible. He is a son of Immer and the great-great-grandfather of Maasai, son of Adiel, son of Jahzerah, son of Meshullam, son of Meshillemith. We know about this Maasai because he is one of the priests who returned from the Babylonian exile (1 Chronicles 9:12).
Nehemiah mentions a Meshillemoth (משלמות), also a son of Immer, who was also an ancestor of a priest who helped to restore the destroyed city of Jerusalem. Most commentators say that this Meshillemoth is the same as Meshillemith but that is by no means certain.
The priest who worked on Jerusalem's fallen structures was named Amashsai, his father was called Azarel, his father Ahzai, and his father Meshillemoth, and that is one generation less than exist between Meshillemith and Maasai. Even if Meshillemoth and Meshillemith (and the two Immers) are the same, then Amashsai may have been Maasai's distant cousin. But there is no evidence for this.
🔼Etymology of the name Meshillemith
The name Meshillemith appears to be derived of a plural participle of the verb שלם (shalem), meaning to be unbroken or whole:
For a meaning of the name Meshillemith, NOBSE Study Bible Name List reads Recompense (which is rather curious because it omits the plural; NOBSE reads Acts Of Recompense for the highly similar name Meshillemoth).
Alfred Jones (Dictionary of Old Testament Proper Names) makes no distinction between the two and reads Those Who Repay for both.
BDB Theological Dictionary translates neither name but does list both under the verb שלם (shalem).