The identification of parts on an overview is done using SOLIDWORKS part numbers. Basically, it is SOLIDWORKS that is responsible for assigning an item number to identify the part in the BOM. When creating the bill of materials, I ask to freeze the numbering (so that it doesn't change completely if I make a change in the assembly (removal of a part, addition of another part etc.)
This works fine except that if I renumber a part or move it, solidworks considers it a new part and reassigns a new part number.
So how can you do this kind of manipulation without him numbering the part in the nomenclature?
I think you're talking about the assigned item number in the assembly, in which case there's not really a solution. Here he proposes 2 things (last message):
Make a print or screen print to rearrange by hand.
Or choose the "Follow assembly order" option and reinsert the part in the same place: