how do you make it so your last name does not show up on facebook to anyone?

[confused composing]

You have to fill in the box of Last Name, whatever it's you fill in there FB can't detect it, remember FB in here is just a program to detect is there something in that box or not, so for instance you might fill it with abbreviation of your last name, that is you give true information right.

And for your information, in my country, not everybody has last name (=family name), many of us even only have one name! That's never comes to FB mind!