You are correct that the name on line 1 of the W-9 is (or should be) the entity’s legal name, and it’s this name that the IRS will match against the tax ID. So you want to be certain that the 1099 reflects the name on line 1.
Many companies have a “DBA” name—a “doing business as” name that may be a brand or shorthand name—and that ordinarily is listed on line 2 of the W-9. It is possible for a company to have a few DBAs, which sounds as though it might be the case here. And it’s perfectly fine to make checks out to the DBA names; but you have to report on the 1099 using the legal name.
While the only “rule” is to report using the legal name and tax ID, if that remit name is not currently on the W-9, it would be a good idea to have some documentation that the name on the invoices does belong to the legal entity. We recommend you ask for another W-9 or other documentation such as a letter, with a list of names it uses—as you suggest—confirming the connection between the DBA and the legal name and tax ID for the company you are paying.
I notice that you say the payee in question is a corporation. Just a reminder that corporations are exempt from reporting, unless they are attorneys, or are providing medical services.
However, you still want to be clear in your records about whom you are paying.