Form W-8BEN and W-8BEN-E

A US payer has to withhold 30% on certain US-source income paid to a foreign person, such as royalties, unless the payee certifies that a lower treaty rate applies. Form W-8BEN does that for an individual, and W-8BEN-E for a company. The IRS looks through a single-member LLC owned by a foreign individual to its owner, so the owner gives a W-8BEN in their own name.

Payments for services performed outside the US aren't US-source and aren't withheld on, but the form still certifies who you are.