The name Zebedee in the Bible
Zebedee is the husband of the only Biblical Salome and the father of James and John, who are also known as Boanerges. We don't know much about Zebedee, but Jesus calls his two sons right out of the family fisher boat, and when they follow Him, Zebedee isn't reported to put up much resistance (Mark 1:19-20). Perhaps this is because he also believes in Christ, although he's never mentioned as one of the disciples. Or perhaps his initial objections were overruled back home by his wife Salome, who is mentioned among the disciples, but who is also quite a impetuous character, and probably best agreed with.
Etymology of the name Zebedee
There's nothing in the Greek language that looks like the name Zebedee (or rather Zebedaios) and Zebedee is most probably a transliteration of the very popular Hebrew name Zebadiah, says Spiros Zodhiates (The Complete Wordstudy Dictionary), or rather, the truncated version Zabdi, says BDB Theological Dictionary.
The name Zebadiah consists of two elements, the final one being יה (Yah) = יהו (Yahu) = יו (Yu), which in turn are abbreviated forms of the Tetragrammaton; the name of the Lord: YHWH.
The first part of the name Zebedee or Zebadiah comes from the verb זבד (zabad), meaning to give:
The whole name Zebadiah and thus Zebedee means Yahweh Has Bestowed (NOBSE Study Bible Name List), Yah Hath Bestowed (BDB Theological Dictionary), or Gift Of The Lord (Alfred Jones' Dictionary of Old Testament Proper Names).