🔼The name Jehudijah in the Bible
There is some discussion about whether the name Jehudijah actually exists in the Bible, and even if it does, whether it shouldn't be Hajehudijah (היהדיה, as per JSP) rather than Jehudijah (יהדיה, as per KJV and Young).
If (Ha)jehudijah is indeed a name, it occurs in 1 Chronicles 4:18, where some hard-to-identify man has a wife who bears him Jered. In the next verse, we meet the wife of Hodiah, or so it seems. The Hebrew also allows that Hodiah is actually the wife, of yet another mystery man. And then there is the Naham of verse 19; somebody is his sister.
Jones' Dictionary of Old Testament Proper Names holds that the Ezrah of verse 17 is the mystery man, his wife is Hodiah, a.k.a Jehudijah, who is the sister of Naham. Or at least, so it seems. Under Jehudijah, Jones proclaims her to be the wife of Mered, who in verse 17 marries Bithia, the daughter of the Pharaoh.
The overwhelming majority of modern commentators, however, see no name Jehudijah, but an adjective meaning Jewish. Their version is that Ezrah has a son Mered, who marries an Egyptian wife and also a Jewish wife. The Egyptian, named Bithia, bears him Miriam, Shammai and Ishbah; the Jewish one bears him Jered, Heber and Jekuthiel.
🔼Etymology of the name Jehudijah
Whether Jehudijah is a name or a regular word, it surely has to do with the name Judah. The first element of the name Judah and thus the word jehudijah is a name-part itself: יה, the commonly accepted abbreviation of יהוה, (YHWH), the Name of the Lord.
The second part of the name Judah comes from the verb ידה (yada), meaning to praise:
The proper adjective that's derived of the name Judah, and which is commonly translated with Jewish, is יהודי (yehudy). To make that word feminine, the letter he should be suffixed, but in our word Jehudijah also the waw drops out, and that's why some people insist it's a name rather than an adjective. And since it has no waw, the name is really (Ha)Jahdiah.
All and all, the name Jehudijah (or Jadiah) means Praise Yahweh. After all the fuss, Jones' Dictionary of Old Testament Proper Names lamely translates this name with Jewess.
Another name that literally means Jewess is Judith.