As a sole trader you could do the following. For £200 you can register a trade mark which you could also use as your business name ie MR MAGIC CARPET.go on to the patent office web site
www.patent.gov.uk Prior to sending your £200 make sure there is not a similar name on this site and the companies house site
www.companieshouse.gov.uk.
otherwise your application will be rejected and you do not get your money refunded.It takes a few month before you find out if it has not been opposed
meanwhile you may use the name.If you need any further info on this let me know.
Paul