Which form to register for self-assesment on foreign income?

Hello, I'm just starting a company in the USA (a pass-through entity), and I'm expecting to have a profit, which will require me to fill out a self-assessment next year. To my understanding, I have to fill out Form SA1 to register for self-assessment due to my foreign income. Is this correct? I'm asking because some people are suggesting I should register for self-assessment as self-employed, which makes no sense to me, as I'm not becoming a sole trader (I won't be working under my own name or operating in the UK; I just need to pay tax on foreign income from a percentage of shares in a foreign business).

`Hi
As it is only for the shares income, the SA1 will be correct.
Thankyou.

Thank you for reply. Technically, this is foreign self-employment, but based on the HMRC help section and the notes on the forms, it looks like this income must be entered in self-assessment under "Employment" and if foreign tax has been paid, then additionally use Form SA106 to claim tax relief. That's why I thought to use Form SA1 to register for self-assessment but not to register as a self-employed sole trader.