Male slovenian name.
There is no real origin of the name Aljaž. The name is mostly used in Slovenia.
Because Slovenia is a christian country, the name could come from the biblical names like Elias or Elijah and was later
translated into slovene in the same way as did
the names for example; Mathew - Matjaž or Thomas - Tomaž.
The name Elijah in Hebrew (אֵלִיָּהוּ – Eliyahu)
components ; El (אֵל) = God and Yahu (יָהוּ) = short form of Yahweh (the name of the God of Israel) and together meaning Eli-yahu = My God is Yahweh