How to name a Rig ? How to search an amp ?

To name, hit "Store". Decide if you want to replace the original or create a new, differently-named copy, following the prompts. The naming tools will magically appear.

Use the soft keys above the screen to choose the various sorting filters. IIRC, the main list, the "unfiltered one", is alphabetical by default, as I suspect the filtered ones are too.

You seem to be looking for Slot Name, not Rig Name.

In current software in Performance Mode select Edit, Slot Settings, Rename Slot and enter your preferred name there. Slot name will appear in one of the five boxes representing the Slots of a Performance.

Rig Name can be edited this way: Enter Rig Settings, select Edit Tags, then select Rig Name and hit Edit.