Correct. We can have as many names as we like too.

However there's various documents available that are proof that one is using a name. So for example my bank wouldn't let me change my name unless I present something like a deed poll. Said deed poll is literally just a print out with some stock phrasing and the signatures of two witnesses.

We don't have a central database that covers everyone in Britain (unlike, say, Sweden). If I want to change my name I can just start using the new one. Amusingly lots of people in the UK don't know this and are sure it's not the case. I ended up switching banks because the final straw was how poorly the staff were trained on the subject. My new bank and the DVLA did not have similar weird ideas, thankfully, so now my name is updated on my driving licence, etc..

I mentioned how my deed poll is a print out earlier because so many people seem to think it needs to be something notarised, or on special stationery, or something (usually they're not sure what, they just think it seems wrong). When they consult the law they tend to then have a bit of a laugh with me because the law is indeed a bit mental (such as at the registry office when I got married a few months ago).