Stephen Hawking, the eminent Cambridge professor, applied on the 2 March 2015 for his own name as a trade mark in a number of activities.
You can register your name as a trade mark under UK law, or an agent or company can do so on your behalf. Anyone else trying to do so is guilty of "bad faith". I remember someone coming into the British Library saying he wanted to register the names of the Beatles. We checked, and three, I think, had registered their names (there's certainly Paul McCartney and Ringo Starr).
Hawking's applications are UK00003097042 and UK00003097043 which between them cover seven classes of named activities. Having classes means that a trade mark like Swan can be used for a variety of services or product and not just by one company covering all activities.
If registered, they will only be valid for the UK, but the option is available under the Paris Convention to apply for protection in for example the USA or the European Union provided this is done within 6 months. It is still possible to do so beyond six months, but if someone else applies before you do then you lose out.
According to an article on the LiveScience website, Stephen Hawking wants to trade mark his name, by Tanya Lewis, Hawking's intention is to block someone else trying to use his name to sell in the areas listed in the applications.
A few years ago I posted on my old work blog about David Beckham and his wife Victoria as brands, where they and their advisors made very effective use of the intellectual property system, including registering David's signature. Quite a few people have done so. Paul Gascoigne, the retired footballer, applied for a number of UK trade marks, all now "dead" and not valid, and several bearing his signature, as shown below in the list of results.
He still has a valid registration in Europe, EU010619732.
Other celebrities who have registered their name or signature include Olivia Newton-John, Alex Ferguson, Ozzy Osbourne... and also Ed Milliband, who was registered by the Labour Party in 2011.
I imagine that it gets more tricky in law when the name is of someone who is dead, such as Ella Fitzgerald and Michael Jackson, who besides registrations when he was alive such as a 1985 filing, had a filing made months after his death.
The UK jurisdiction has had a number of disputes about the right to use a name, or a trade mark close to a name, such as Albert Einstein, Jane Austen, Elvis Presley and Marlene Dietrich. There is also a European-wide case regarding Pablo Picasso.
Fictional characters and the names of teams or other entities or television programmes can also be involved in disputes over who has the right to use it in commerce. It all comes under the umbrella term of "character merchandising."
It reminds me of a 1920s court case when a man called Albert Hall decided to form an orchestra. In those days it was normal to call an orchestra after the leader, so he called it the Albert Hall Orchestra. He was taken to court by the Royal Albert Hall who claimed that he was trying to give the impression that he was connected with them. The judge, finding for the defendant, said that if you were called Albert Hall it was perfectly reasonable that you would call your orchestra the Albert Hall Orchestra.
However, a man called Henry Harrod who opened a business in New Zealand and called it Harrods was opposed by the famous department store. Apparently people might have thought that there was a connection. The action was dropped when many businesses in the town changed their name similarly, and indeed the town changed its name temporarily to Harrodsville.