I think you are right, but I have one of those already, for a community site I run, and it would have the "wrong" name on the payer's statement for this new purpose, which is a private website, no person's name associated with it, so just the domain name really. The PP business account shows on a statement as XYZ Ltd which is the name of the Ltd Co I set up to run that community site, so useless for this purpose.
The problem is that one can go all the way through the huge hassle of setting up yet another paypal account, only to find that you cannot configure this aspect. Online info is really ambiguous.
If the name on the statement is not a very obvious match for where you made the payment, you get a 10-20% rate of "fraud" reports - I found this on another project.