I think I have done both in the past, there’s a few subtle differences on why though. One company was just entered in my supplier list as their trading name, no specifics, no company info or anything, just a single name. When they got bought out their invoicing was the same, just now it said they were owned by this other company. Even if I would have entered them on the system now I would not have done anything differently, I am still dealing with the trading name not the limited.
If you actually check a lot of your suppliers you will probably find you aren’t actually dealing with the company name but some other ltd/plc.
From the point of view of the name in Quickfile it makes no difference whatsoever though either way, it’s the figures that count and if anyone ever looks into your history with the company the associated invoices will show exactly who you dealt with. The names in Quickfile don’t even need to match the names of the company the invoice is for as it is just for our own reference. Lots of my receipts are just under various miscellaneous account names.