I'm in the US, so it's a bit different. (I don't know about any "registering"). But my son is diagnosed with AS, and as such, he is legally entitled to an IEP (Individualized Education Plan). That's a big deal. We sit down with the teachers and principal every year (or whenever necessary) and make sure he's getting whatever special accomodations he needs. That can include training in AS for the teachers, being exempt from timed tests, being allowed to go to a "safe" place when he gets overwhelmed, and things like that. In the US, every kid (until age 21) who is diagnosed with autism is legally entitled to an IEP, and as long as the school plays by the rules, it can make the difference between the kid thriving or slipping through the cracks. And since it's a federal law, they can't say, "Oh gee, we don't feel like it." A whole bunch of people on this board are legally entitled to an IEP, and probably don't know it. I'm sure the UK has a similar thing.
I have never had the feeling that is disadvantaged by having a "label". It's wonderful that he gets the help that he needs. The "label" is confidential anyway.
I suggest getting to know the details of special education laws where you live. If you were in the US, I'd definitely say tell the school, and get the individualized help your son is entitled to.