I was named for my paternal grandmother in the Greek tradition. When it came to a middle name, my mom wanted to give me my great-grandmother's name, Angelica. My dad wanted to follow Greek tradition again and give me the feminine version of his name, which would have been Sotiria.
Thank goodness, they could not come to an agreement so I ended up with no middle name at all. After I got married, I took my maiden name as a middle, which I think is a very happy compromise.