The label name shown in ladder logic will not update automatically, even though the label in the I/O table has changed (in this case the new function name).
You only need to double click on the function in ladder logic that displays the old name and it will bring up the label editor so that you can enter the new function name. The next time you double click on it, the new function with the new code will open in the function editor.
[Edit 2015-6-4]:
1) You can easily change the label of any element in the ladder logic program by selecting it and then press the "E" key on the keyboard, which will bring up the label editor prompt.
2) You can also find all the old label names on the ladder program and replace them with new label names using the "Edit->Find (Ctrl+F)" function.