Question: I own a domain, which I will call example.com.

In June, I received an email, purporting to be from the Play Station Network, addresses to first.last@example.com. (I receive all the email for the domain. "First" and "Last" are distinctive names which are not my name.)

It was an account registration confirmation. I wasn't sure how anyone could have signed up as first.last@example.com, as it's my domain and most web sites require a confirmation link to be clicked.

I changed all my passwords, just in case.

first.last@example.com then opened a PayPal account and has been successfully sending small (~$10) payments to MicroSoft Payments and other vendors. No money has been stolen from me, yet, so I have no reason to involve the police.

I sent these emails to PayPal's fraud address, but I was ignored.

Today, I have received multiple emails from PayPal saying that "my" bank has declined payments. Once again, no money has been stolen from me.

What is going on? I am nervous that I am being targeted for a scam.

Thoughts:

1. If they actually had access to my email account, they could have reset my passwords and stolen a few domains from me. This has not happened.
2. Are any of the emails that I've received at first.last@example.com actually from the purported senders? They all seem to come through mail2world.com and have a open, red padlock in gmail.
3. Who can I contact about this to have it stopped? PayPal do not respond. Should I contact the companies they've paid?

Answer: 
You've been targeted by an attempt of phishing. Nowadays it's quite easy to fake an email from PayPal etc.

So they're trying to make you believe that you need to click on the links from PayPal and login to figure out what's going on. Don't ever do that. If you did, change all your passwords quickly.
It's hard to say if this is a scam or not because of the, um, free-wheeling way PayPal does things.

Someone recently opened a Paypal account using a secondary email address of mine (one that Comcast forced me to create, and which was in a recent breach). Paypal *does not confirm* they have access to the email, but lets them set up an account and add a phone number for confirmation, making it impossible for me to just reset the password and close the account.

Paypal is remarkably reluctant to do anything about this; I've not been able to get them to do anything at all in several months. So far the person using the account has not defrauded anyone, but who knows. Try calling Paypal and insisting to speak to someone in the fraud department, and mention that you are planning to report this to your local police or the FBI if they don't do something about it. Maybe you'll have better luck.