Is It Required By Law to Include My Real Name in Paypal Invoices?

Hi guys!

First of all, I am not from the USA, I am from a small European country that is a part of the European Union. However, I often come in contact with people from all over the world and do business with them. Many of my customers are from the U.S., others are from the UK and some are from non-English-speaking countries.

My question deserves a bit of an introduction so let me do so: I have several lines of business, each of which uses a different business name, email address and contact information. I would like to ask you if any one of you know whether it is possible, in legal terms, to include a different name for every Paypal invoice that I create? Or perhaps a better way to put it would be: Is it OK to use a unique name for every unique customer who purchases my services whom I invoice via Paypal?

Before posting this question on the WF, I was wondering whether Paypal itself would be OK with it, so I reached out to them and asked one of their representatives. He said that from a payment point of view, it doesn't matter if I change my name, contact information, business name and email for every invoice that I send out. Well, this is only a payment point of view, though, and I can clearly understand why Paypal do not care - they simply want their cut of the transaction, it doesn't bother them whether the name is my real name or a pen name.

However, what Paypal cares or doesn't care about is one thing but the law is a completely different ball game. The law might prescribe that I must include my real name in the invoices that I send out. So I wanted to ask if you know what the law says in this regard and which law (whose country's law) would be used if I, as a service provider, send an invoice to an American citizen - would American law or my local law be applied on the transaction to determine possible legal obligation to include my real name?

Thanks a lot for reading this and hopefully commenting on it!