You can de-list pretty much all information about you - without a publicly visible profile picture and your current location (city/country), you're pretty much impossible to find among others who share your first and last name. And yes, Facebook has enough users now that if you live in a big city, it's likely you'll find a few people sharing your first and last name in the same city.

Unless you have a very uncommon name, or live in a smaller city. I live in a 280k city and everyone with my last name in the phonebook is related to me, and on Facebook only me, my sister, my uncle and my cousin have an account.

My full name exists less than a dozen times on Facebook in all of Germany, and the name does not occur anywhere in the world outside of northern Germany.

This is quite an issue.

I know many people with highly distinctive, and, in a surprising number of cases, entirely unique names. Some rather surprisingly.

Name plus city plus one other piece of data (approximate birth date, school(s) attended, former employer(s), a few other associates/contacts, profession) are very often enough to uniquely identify an individual, even with an otherwise common identity.

> (approximate birth date, school(s) attended, former employer(s), a few other associates/contacts, profession) are very often enough to uniquely identify an individual

Yes, but you can set all of those to private and thus effectively delist yourself from Facebook Search. The only thing that really has to be public nowadays is your name.