The name Haggai in the Bible
The name Haggai is assigned to only one person in the Bible, although the name Haggi is pretty much identical to Haggai. Haggai is a minor prophet of Israel who wrote around 520 BC, the time when Israel had returned from exile and was recreating the country (Haggai 1:1).
Haggai's book is one of the shortest in the Bible. It consists of only 2 chapters, a total of 38 verses, and it's entirely directed at Zerubbabel, the son of Shealtiel, governor of Judah, as God wants Zerubbabel to rebuild the temple.
Etymology of the name Haggai
The name Haggai is quite possibly derived from the Hebrew verb חגג (hagag), meaning to celebrate:
Post-fixed with the possessive yod the name Haggai may mean My Feast. But the yod may also create an adjective, which appears to be preferred by scholars: For a meaning of the name Haggai, BDB Theological Dictionary reads Festal. NOBSE Study Bible Name List reads Festive.
Jones' Dictionary of Old Testament Proper Names assumes that Haggai is an abbreviated form of Haggiah and that the yod is a remnant of יה (Yah) = יהו (Yahu) = יו (Yu), which in turn are abbreviated forms of the Tetragrammaton יהוה, YHWH, or Yahweh. Hence Jones translates Haggai with Festival Of The Lord.