ChainJane It's closer to calling Richard Bachman Stephen King or Robert Galbraith (or even JK Rowling) Joanne Rowling. It's a known work name, and in the UK it would a legal name he's known as, but in most of the reporting on this it uses both names because the courts have to use Stephen Yaxley-Lennon - it's the name on his paperwork (and actually, even his frequent use of Tommy Robinson doesn't mean he 'prefers it' in his personal life).
People who use multiple names, work names or pen names are aware of the names on our paperwork that would be used for passports or, in this case, a legal proceeding(though it can be complicated if for some reason someone has multiple names across different legal paperwork -- I thankfully didn't have when I had that issue for a few years, but I'm not an asshole who ends up repeatedly in court for saying shite).
I do have some mild discomfort with 'real name' or 'legal name' because I've legally changed my name and people often use those terms to mean the name on my birth certificate (which I wasn't even raised with) and I view all the names I have used in real life as my real names, but there isn't really a better term for when someone uses a different names to the one on their paperwork. It wouldn't be misnaming me to use the name on my passport, and I find the comparison to trans or other dysphoric people who've changed their names for their own comfort compared to this guy mainly doing it as part of an act highly questionable.
Oh, and Caitlyn Jenner has referred to their younger self as Bruce and I believe has mentioned not minding it to refer to the sporting career and things (I don't really follow that, but I remember there was some controversy over the fact Jenner didn't follow the deadname idea and I liked the publicity on how there are many ways people view this rather than just the Twitter rhetoric), but yes, it would be rude not to use the name someone has introduced themself as or changed their name to - and the court 'introduced' him as Stephen Yaxley-Lennon.