Separation of church and state is not in the Constitution. The closest you will get is the first amendment, which prevents Congress from establishing a religion, or preventing the free practice of one.
I’m with you that religion should not be forced in schools, but you can’t use the Constitution to prevent this particular issue.
That is a bit of a selection bias. What you are effectively saying is “the biblical names that have survived to today have staying power”.
But even that isn’t true here as almost all of the names you cite are significantly different now than their original forms. Looking at your list we have Yeshua, Shemuel, Mikael, Rivka, Yohanan, Miriam, and Paulus. Adam is mostly the same, as is David (with a bit of an accent difference), but the rest didn’t exactly emerge as they were.