The name Ezekiel in the Bible
The name Ezekiel is assigned twice in the Bible. The lesser known Ezekiel is a priest in the time of King David (1 Chronicles 24:16). In English Bibles this man is often referred to as Jehezkel or Jehezekel, but in Hebrew his name is identical to the famous Ezekiel. And the famous Ezekiel should be called Jehezkel or Jehezekel as well, because that's a much closer transliteration. But we're used to Ezekiel, so Ezekiel it is.
The famous Ezekiel is the author of the Book of Ezekiel, and a major prophet of Israel who lived and worked among the exiles in Babylon. A curious detail is that the name of Ezekiel the prophet is mentioned only two times in the entire Bible, in Ezekiel 1:3 and 24:24. To compare: the name Isaiah is mentioned 53 times and Jeremiah a cool 145 times.
Etymology of the name Ezekiel
The first part comes from the verb חזק (hazaq), meaning to be strong:
For a meaning of the name Ezekiel, BDB Theological Dictionary proposes God Strengtheneth, and NOBSE Study Bible Name List reads the similar God Strengthens. Jones' Dictionary of Old Testament Proper Names has Strength Of God, God Strengthens or Strengthened By God.