https://assets.publishing.service.gov.uk/government/uploads/...
These Deed Poll forms are produced by any number of paralegal-esque companies and are useful to include when writing to your bank/utility conpany, but that's about it.
https://www.nrscotland.gov.uk/registration/recording-change-...
Edit: Being married to Scots law lawyer I feel obliged to point these things out any time I see a mention of a "UK" legal system... ;-)
Perhaps the next logical step for this comedian is to find a class in which Hugo Boss is not registered and register his own trademark in that class. Then he can give himself permission to use his own name. Or something. I actually have no idea how the rule in the the linked document would be applied in practice. Perhaps in practice they don't care about trademarks if the name is an ordinary name, like "John Smith", for example. Which is almost certainly also a trademark ... I've just checked (https://trademarks.ipo.gov.uk/ipo-tmtext): JOHN SMITH matches a bunch of different trademarks, and if you include JOHN SMITH'S then there are even more of them.