A change of company branding, or even a complete takeover of a company, doesn't affect your right to claim back mis-sold PPI.
I received a letter from a firm I'd never heard of relating to missold PPI. I assumed it was just another company that wanted to try to claim back PPI (for a big share of the money) on my behalf and ignored it for several months. When I found it again (under a pile of papers, during a rare tidy-up of my living room) I saw that it was from the an American firm which had taken over the company with whom I'd had a credit card many years before. The letter invited me to make a claim for any PPI that I thought might have been mis-sold to me and to enter a security number online if I wanted to do so.
I never intended to make a claim (as I didn't think that the PPI I'd had had actually been 'mis-sold') but, just out of curiosity, I went online and entered the security code. I was expecting to be asked loads of questions about why I thought that the PPI had been mis-sold but, instead, I just saw a message saying "Thank you for submitting your claim. We'll be in touch with you shortly". A few weeks later I received a cheque for £3k ;-)