Information needed for charges without tax

I've been working part time as a sole trader for the past couple of months. I'm doing a college course full time, receiving an allowance for this from welfare, so not registered for tax for now. (I'm planning to be set up as a full time sole trader later this year.)

I just need to know - when sending an invoice to another sole trader who is registered, what details are required to be included about myself so their accountant can record it as a cost?
Would my firstname, lastname and a provisional name describing the business(haven't registered a name for the business yet) and phone number suffice?

No. Your name, address and PPSN are required. You cannot charge VAT on these transactions as you are not registered.