“Genesis” is now in the 2014 top 50 baby girl names in the US. It’s apparently been hanging around since 1998.
I find this a rather charming name, actually. It’s Greek for “beginning” (as in “In the beginning….”), it’s Biblical, and it has a pretty sound. Probably most girls who are given the name will be nicknamed Jenny or Sis, which is perfectly in line with American naming practices.
There’s a minor tradition among people in Bible churches of picking out Greek and Hebrew words from the Bible to name their kids. I don’t know if this is an example of that or not. There are apparently some Spanish-speaking families picking this name, too.
We don’t really have a Bible feast day. (No “Exaltation of the Holy Bible” or anything like that.) So if I had to pick a name day saint, I’d pick a matriarch or patriarch from the Book of Genesis. For example, St. Adam and St. Eve are on December 24 (in anticipation of Jesus’ coming on the 25th).