We use ebay quite a bit. You don't have to use paypal, you can ask for a direct money transfer, or if they are collecting it, ask for cash. But then again, you shouldn't send it until you have received full payment, that's how I understand ebay works anyway.
But in answer to your question, see paypal as a bank account. Someone can pay in whatever they want on your behalf, and if they want to pay more in later, that's fine. It is completely independent from ebay, so what goes into paypal doesn't have to be the asking price, and I think you can amend the item in ebay showing that part payment has been made.
But I stress, I would not send anything until full payment has been received.