Finally found credit agreement and it is in a different name

I wonder if I have missed my chance.

I went through Gladstone Brooke’s to reclaim ppi on a loan I had with Abbey National (now Santander)

I knew I had ppi on it but the response was I didn’t have ppi with them.

Before I go on I have to say Abbey/Santander have real difficulty with my name.
It isn’t a particularly unusual name. It isn’t a hard to spell name but I have given up trying to get them to spell or even get my name correct.
For instance neither my credit or debit card have my actual name on them. They aren’t even matching. I get called a variation of my name all the time with them.

Going through a box of stuff I found the original credit agreement.

Account number
How much ppi was charged
Everything including my surname (which is correct) and a first name that sounds similar to my name but isn’t (like my name being Petra and they have it down as Peta but a little more wide of the mark and a few more different letters)

Can I go back to them with this new information given I did technically start this claim back in May and they do not have my name correct on the paperwork.

FWIW I have tried in the past to get my name corrected but they have lost important documentation when I have sent it in to them to prove what my name is and either not done anything or corrected it wrongly.

Thanks for any advice on advance