I don't think you can copyright a Trade name. You can register it though but only if it's a business name ie the name of your company. last time I did that it was £150 but it probably costs more now. (to set up a company that is) there are loads of places that are on the net which will do it for you at a price or you can do it direct with Companies House ( ie the government) fairly straightforwardly. once you have registered your company name no one else can use it to trade. If it's a logo or other bit of artwork you have designed you include the little © sign and that "asserts your intellectual rights' which means no one can use it without your permission (in theory)
It's not really something you can do on the cheap, as forks said you register a trademark. Everything (including a company name) is in theory copyright if you say it is, the purpose of registering it is really to give any other companies the chance to block it if they feel it is close to their mark within one of their nominated business sectors. As I recall the process costs about £500, it's been a while since I've done one however.
that's partly true but the other purpose of registering it is so you don't inadvertently start using someone else's trade name and get sued. and not everything is copyrightable either - it has to be original ie not copied either whole or in part and it can't be generic either
the companies that do it for you buy up failed company names, and then you buy one of them off the shelf, and they change the name for you to one you want. it's very quick and simple. If it's a limited company you need 3 shareholders one of whom is the company secretary. Or you can just be a sole trader as in 'mr technofish, pike fitter' https://www.incorporateonline.co.uk/?gclid=CKav2v2x9JICFRNPMAodvUH0wA for example
Mines limited and i only have 2 shareholders. Myself as the company director and partner as company secretary. I get to pay her a wage also so paying less tax as she can offset it against her personal allowance.
a company doesn't have to be limited. A trade mark a copyrighted logo and a trade name are different things.