Building on what mevaqesh said. The names are borrowed directly from the pagan Babylonians. Some of them are actually names of foreign gods. Like the month of Tammuz, mentioned in Ezekiel 8:14. I don't know if Iyyar happens to be a name of a foreign god, but maybe you could look into that. But I can guarantee you that when the Babylonians decided on naming the month Iyyar, there was zero possibility that it had anything to do with the tetragrammaton, or the Israelite people. Therefore, I doubt there's any reliable source that says that Iyaar stands for a phrase from the Pentateuch containing the tetragrammaton.
If you would like to know what the Bible called the month of Iyyar, it's called זו as is mentioned in 1 Kings 6. Maybe you can write the author of The Wisdom in the Hebrew Months and ask him what significance זו has.