A while ago I asked my GP to change my title of address from "Mr" to "Ms". It turns out whatever system the NHS (or possibly just my GP's surgery) uses to keep their records absolutely didn't expect that and has no provision to handle it. I bet it's perfectly possible to change from "Ms" to "Mrs" or even from "Mr" to "Fr" or "Dr" but try to go from "Mr" to "Ms" and the whole thing HCFs. So there's now two records for…
This can lead to some onerous requirements when people want to change name.
Your GP surgery should have a system for gathering patient feedback (it's something the CQC looks for) so you can try using that.
If you don't get anywhere with their process you could try your local clinical commissioning group.
If you wanted to go the technical route you could ask what software they use, and find a user group for that software to ask how it would be done.
Of course, you shouldn't need to do any of that. It sucks that they're making you jump through hoops.