I am aware that as a Limited Company I would have to register my name with companies house, BUT how to I go about registering my company name as a Sole Trader?
You need to register your name as trade mark, that's all, protecting your identity is vital - see our website at www.crossguard.info, it's not fancy but it's got all you need to know.
In a nutshell, you can't register your name as a sole trader. You can only register a name as a limited company. If there is something special about your name that you want to protect, then as Philip says you can register it as a trademark, but most sole traders simply trade as they are. You should however check whether the name you intend using is trademarked - have a look at http://www.patent.gov.uk/ Be aware as well that you do need to inform the Inland Revenue within 3 months of starting trading as well.