This is actually not definitively possible. You cannot prove a negative.
Let's say that you decide on the name Abcde, as there is no religious source material that uses that name and the etymology is non-religious.
How do you know that there won't be a future discovery of a religious text in which the name Abcde is used? Now what?
On a different thread, do you put a statute of limitations on what you call a religious link?
The name Amun has religious etymology, but it is of a religion that hasn't been actively practiced for millennia (Ancient Egypt) - how do you feel about that? (regardless of whether you like the name, for the sake of the example)
At what point (if ever) do you accept that a name with a religious origin may be absorbed into cultural history without particularly maintaining its religious link?
It seems to me that you're better off tackling this the other way around. Find a name you like, and look into its etymology. If you don't like its etymology, find another name. If you're okay with its etymology, maybe that's the name you want to pick.
Doing it the other way around by first generating a list of all the names that match your criteria first requires you to precisely denote your criteria and assume that all the information regarding a name's etymology and usage that you have is completely correct. That's a tall order.