It doesn't matter. They should put their name on the W-9 the way they want the payer to put it on checks and 1099 forms.
You are talking about Form W-9 that they use to provide their tax ID number (SSN or EIN) to a client or someone else (but not an employer) who is going to make payments to them, is that right? Who are "they," and what is their connection to you?
