I don't think you need to be a business.
I've used business services a few times, some long before i was self employed.
Under business name i just put my name, just like a self employed sole trader would.
The only real difference is you get a bill with a vat receipt so you can claim stuff back in a tax return.
If you don't need do a tax return then just bin them.
There's usually no special requirements like being a registered business or vat registered etc
I've only ever seen that being required for expensive leased lines and is probably more to do with running a credit check on the business.