Re: No, this computer is not for personal use - it's my woke one.
You aren't allowed a business name such that someone could commit a crime by uttering it aloud, so it would not be a massive stretch to block a business name that someone could commit an offence under the misuse of computers act by entering into a computer.
On the other hand, a Companies House employee entering a name into a Companies House computer in the course of their regular employment probably would not be unauthorised, so there still might not be any offence committed.
And if we do end up with a new law to prevent this, it's almost certain to be unfit for purpose .....