When you run a filter you will create a new probe list. You will always be prompted for what you call your new list although a default name will be provided.
Probe lists go into your Data View, and are always stored in alphabetical order. If you select a probe list in the Data View then the chromosome view will change to show you just the probes contained in the list. Any further filters you run will also use the current probe list as their starting point and any lists they create will be a subset of the currently selected list.
Probe lists only apply to the current ProbeSet. If for any reason you choose to redefine your ProbeSet then you will loose all of the probe lists you generated with the old ProbeSet.
If you want to rename a probe list you can do this by right-clicking on it and selecting rename. You can right-click on a probe list and select delete to permanently remove it.