it will still have the same name, it's just stops broadcasting it's name, you don't delete anything.
just check the box.
on your devices that have already connected to it will still show the name in the wifi list, and connect to it as usual.
on you devices, if you "forget this network" then the name won't show up anymore.
of if a device has never connected to the network, the name won't appear in their list either.
Hiding your network really doesn't do much for security, scanning software that is easily accessed will show the name.