A supplier business name, telephone number and address is a requirement for CLP labels. If you are the one creating the product and selling it, then it is your details that need to be on the label.
By law, customers need to know who they are transacting with. If they need to contact you, they can easily do so via the details on your item.
Regardless of whether you have business premises, you do need to provide a legal owenership name, a geographical location where documents can be sent, and a telephone number.