We named one of our kids after a greek letter and the other's name means lion. Each name has significance to us, lots of nice nickname potential and they are both fairly unique.
That said, I originally wanted to name the kids after dead physicists and mathematicians, a la Feynman, Sadi or Pascal. Gauss was a little too much.
I guess my rules aligned with yours tele (though we kind of botched #1 with one kid), with the exception of #3. I don't know that we got that systematic about finding unique names.
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