If you are attempting to pay a sole trader or partnership, that is not registered with Companies House, they will not appear in the supplier list when you search for them.
Please see the article on adding a sole trader or Partnership.
If your supplier is registered with Companies House, please ensure that you are typing the full company name exactly as it's listed with Companies House and pressing the search button. Also please note that currently if an abbreviation such as ltd. is used in place of limited this will also hinder the search function. If you still can't find the supplier then please get in touch with [email protected].