I use the "Name Selection in Column..." feature all the time... I also delete the value of 0 in the "Unselected" field all the time so that any pre-existing values in my "Label" column will not be overwritten by that 0.
When I first started using this fantastic feature I frequently made the mistake of hitting the Enter/Return key as soon as I finished typing a string into the "Selected" field... and each time I would lose all the data I had previously written to the "Label" column. I don't make this mistake anymore, but I'm sure many new JMP users do.
I'd like to suggest that the default value for that "Unselected" field should be no value at all, consdering how relatively easy it would be to type "0" when that's actually (but rarely) the desired behavior, and how relatively dire the consequences can be when that is (almost always) not the desired behavior.
This is currently what users see when they open this modal: