My cat's name is Inky (her full name is Inklila Brynn) and we sometimes call her Inka as a joke. I had no idea this was a real name! I know about the Incas, by the way.
To be honest, this name suits girls under the age of 16 better than women. I have a very hard time picturing a 45-year-old woman named Inka, and I swear it's not just because this name is common on people born in the 80s.