@Alissa35 No, there is nowhere else to name it to make it easier to search. However, if you have a distinctive name and you Google the property name (in my case The Flat on King Airbnb, or Sherkston Paradise Airbnb for my secondary listing), it will come up as the first result.
Also, in future, Airbnb will be offering custom URLs so your property, so you could get www.airbnb.com/h/sherkstonparadise , for example, which should make it easier to brand and for guests and friends to find you.
I really love giving properties names, and really, I think it can only help differentiate you from the competition.