What do you mean with "Icon Name"?
The Text under the Icon ist the Name of the Object.
You can change it with:
objectname.name := "xy";
if you want to this a second time please consider that the new "objectname" is "xy";
As far as I know, there is no way of doing this (though I also do not know why you would want to do it). Anyway, the functions createIcon, deleteIcon and existsIcon can be used to generate icons with a specific name.