Genesis is >from Greek not Hebrew. The Hebrew name for the book of
Genesis is b'reishit, whose root is resh-alef-shin meaning head or top.

As far as I know, Genesya is of Slavic origin, and it's possibly linked
to Hanna (at least by sound), since Russian usually changes the "h" to
a "g". The "ya" at the end would be a usual Slavic feminine suffix
rather than a reference to god, as in many biblical names.

But the link to Nehama still seems to be mostly empirical.

tom klein, Toronto