No, you CAN NOT protect a name using copyright and Protect My Work. Copyright law does not protect names or slogans, but we can protect original logos.
For a name:
For questions specifically about names, please contact the UK Intellectual Property Office:
Website: www.gov.uk/topic/intellectual-property/trade-marks
Email: information@ipo.gov.uk
Telephone: 0300 300 2000
Outside the UK: +44 (0)1633 814000