No -- one of the only true advantages to PayPal is the ability to add multiple websites to the same account for processing. I routinely add and remove payment address in my PP account as I experiment with niches, set up little short-term sales sites etc. The name on the bank account is a company name which bears to resemblance at all to the various payment addresses.
Right, the payee e-mail address and name can be anything. I'm not sure how strict they are on the registrant and bank account names matching -- my main bank account matches the registrant, but there are two other bank accounts attached that have different names -- so you can have different names on the accounts, but the main one may have to match the account holder name (I'm sorry; just not sure on this point.)