In the UK “real name” and “legal name” are just aliases for “your name” which is the identity you’re known by on documents issued by the government and its Home Office, ie your National Insurance record or your UK Passport. Your aliases are not your name unless and until you change that name by deed poll or through marriage / divorce. Your aliases, no matter how well recognized they may be, are
not your name.
The idiot whose name is Stephen Christopher Yaxley-Lennon is also known by the alias Tommy Robinson, amongst others. The aliases exist to protect the identity from the legal and moral consequences of the idiot’s speech. While I’m not sure there is value in always reminding every audience of the real identity every alias refers to, in this case he’s got a history of intentional name obfuscation.