🔼The name Shabbethai in the Bible
There's probably only one man named Shabbethai in the Bible, but he appears in three unrelated events. Ezra mentions Shabbethai the Levite as one of the four braves who dared to oppose the mass-divorce that resulted from the purge of Ezra (Ezra 10:15).
Nehemiah mentions Shabbethai among the small group of men who explained the Law to the people, accompanied by Levites, (Nehemiah 8:7), and later as one of the Levite leaders in charge of the repair work done on the outside of the temple (Nehemiah 11:16).
🔼Etymology of the name Shabbethai
The name Shabbethai comes from the familiar word שבת (shabbat), meaning either rest or Sabbath:
The letter י (yod) upon which our name ends, may either create an adjective (Sabbath-like, or belonging to the Sabbath), a possessive form (my Sabbath), or may be a remnant of יה (Yah) = יהו (Yahu) = יו (Yu), which in turn are abbreviated forms of the Tetragrammaton יהוה, YHWH, or Yahweh.
For a meaning of the name Shabbethai, NOBSE Study Bible Name List goes with Sabbath and sees the final י (yod) as an adjective-maker. Adjectives in Hebrew may also serve as ethnonym (ישראל means Israel; the adjective ישראלי means Israeli, or one born in or belonging to Israel). Hence NOBSE reads Sabbath-born.
Alfred Jones (Dictionary of Old Testament Proper Names) goes with the verb meaning to rest, and sees the final י (yod) as remnant of יהוה. And so, Jones reads Rest Of The Lord.
BDB Theological Dictionary doesn't interpret our name but does list it under the root שבת.