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.
The one question that hasn't been answered is how did they fake the email from your domain. That is very simple - they used what's called an open relay. 

An open relay server (most email servers are configured not to do this) will allow emails to be sent from wherever without verification. Think of it as like sending a letter to someone and writing a return address on the envelope - no one can verify this. 

I could send an email from bill.gates@microsoft.com using an open relay. When you look at the headers of the message, you'll see the origin of the email which will most likely be an IP address.