If apparently by paying contactless at one of your cashback retailers a different merchant name, not including the name of your chosen cashback retailer, appears on your receipt, then when paid by Pin and Chip you can always contact support (sending your receipt) and they will still apply the cashback.
I only need to do this once and the next time I go to the same (franchise) shop the cashback is applied automatically…but I have seen reports of customers that had to contact support every single time.
So it’s indeed true that if on your receipt the merchant name does not include the name of the cashback retailer the cashback is not applied automatically.
Myself have never seen that paying contactless or paying by pin and chip made any difference for the merchant name showing on my receipt. So what I am telling here from my own experience is in general (regardless of how I paid) when I paid at a (franchise) store not showing the matching cashback retailer name on my receipt.
So I can confirm the cashback not being applied when the merchant name on the receipt does not include the name of cashback retailer.
I can’t confirm that the merchant name on the receipt can differ depending on if you are paying contactless or by Pin&Chip.