How do I set up as a sole trader for freelancing?

I have a full time job PAYE as a nurse – I have recently joined a private business to mentor and provide training to students online. This is freelance work which I will do sporadically around my full time role. I understand I need to set up as a sole trader via HMRC – do I need a business name? And should I have a separate bank account for this wage to be paid into? TIA