Can I ask how much the fee is that the "broker" is charging the borrower for basically doing nothing for them? This does not sound like how a typical mortgage broker/lender relationship works. Have you reviewed the broker/lender contract and vetted it against the RESPA Statement of Policy 1999-1?
https://archives.hud.gov/news/1999/rspntce.htmlWhile it does not sound like you are paying the broker, I would be hesitant to enter into a relationship with a broker that is charging the borrower directly if they are not "earning" their broker fee under that guidance.
It would be a Section A fee, it would be a finance charge and yes, the name of the originator to whom it is payable must be shown in Section A, if the payment is not to the lender.