I would be so incredibly happy if it was just a random name, unconnected to Khan or a derivation of Arik Soong's ancestry.
I just don't think that's likely. There's no way they didn't know "Noonen-Singh" is Khan's last name and it's a coincidence. There is some purpose behind it. I'm not sold that she's his descendant, and it could be she's genetically altered in a lab and named after him or some such backstory, but it's still quite the coincidence she'd be on the ship that eventually discovers him and then defeats him twice.