For me it seems to be working fine, using JMP16.2.0 Pro on Windows 10.
After pressing Replace, the space will be removed
Edit:
If you are willing to use scripting, you could use something like this (requires JMP16 due to For Each), but of course it would be good to figure out why Find and replace isn't working.
Names Default To Here(1);
dt = Open("$SAMPLE_DATA/Iris.jmp");
//dt = Current Data Table();
For Each({col_name}, dt << Get Column Names("String"),
Column(dt, col_name) << Set Name(Substitute(col_name, " ", ""));
);
-Jarmo