Making a proper statement

When I first became an Amex cardholder, four years ago, my name was spelt wrongly on the newly-issued credit card.*
I called Customer Service, who sent me a new card – which was also spelt wrongly.
I called Customer Service again, and they sent me another card – still, spelt wrongly.
Amex mispellings
Evidence – two replacement cards with my name spelt as “Khim” instead of “Kim”.
Finally they got my name right. Then, when I started using the card, they misspelt the name on my monthly statements as well.
I called Customer Service again, and they promised to fix it.
In the next statement they sent, the name at the top of the document was spelt correctly, but further down, where my name was repeated, the same misspelling prevailed.
It was so tiring that I decided to forget about complaining for a while. It was not a big issue, but I did expect a top-notch company to get their internal processes right. Also, if I ever had to use my statements to make claims, it might look funny that my name was spelt a little differently, halfway down the document.
But after going through my monthly statements today, I felt there was no point accepting it anymore. It’s the new year and things need to be set straight!
So I called Customer Service just now.
I told this Customer Service rep my neverending story – of how I’ve tried in vain to correct the spelling of my name in all documents. This time, I wanted her to fix the misspelt names that still appears in the second half of every page in my statements.
The rep apologised on behalf of her colleagues and promised this would be the last time I would need to call them up about this.
-However, she would have to issue me a new card.
Why? I asked.
-Because the card is linked to the particular field in the statement. Thus, to correct the name in the statement, she needs to send me a new card.
But the name on my card is spelt correctly. Why can’t I just keep my card, and Amex can simply amend the name on the statement?
-It has to be done this way. It’s linked.
That’s strange. If they’re linked, then why is my card spelt correctly but the statement name is still wrong?
-She didn’t quite have an answer for that.
And if a new card is sent to me, will the number be changed as well, or just the name? I had monthly and annual subscriptions online, so changing my card number means I have to update all these website as well.
-Yes, the number would be changed too.
So I can’t use my existing card until you send me a new one?
-Yes, your card will be deactivated. But we will dispatch a new card to you tomorrow.
It doesn’t appear as if your processes are working together efficiently.
(I said something to that effect)
-The rep assured me, again, that this would be the last time I’d have to call them up about this.
I decided to go through with the card change so that I could resolve this problem once and for all. Nevertheless, it amazes me that systems can be so interlinked yet not really talking to each other, at least for the right things.
Taking it a step further – would feedback like mine lead to any systemic change? I really wonder. Maybe if enough people complain about it. Still, you can see how much time and resources were taken up to rectify this mistake, e.g. re-issuing cards and documents, sending couriers, spending time on hold and talking on the phone… because things were not linked up properly.
*For those unfamiliar with Singapore credit card application process: When you apply for credit cards, you need to submit copies of your Identification documents – so there’s no way I’d have spelt my own name wrongly.