Does receiving spam iMessages / FaceTime calls indicate my account is compromised?

In short, your account wasn't hacked or compromised if someone you don't know places a call or SMS or iMessage or FaceTime call to your address.

Sadly, you can't easily block or change your iMessage and FaceTime account today, but if this grows, I would expect a way to block things just like the phone company now has various options for blocking unwanted calls even though they did not have such blocking in the past.

When you register for iMessage, you tell Apple either your email address or your phone number. Anyone else with iMessage can add your email address or phone number, so in that respect this is exactly like email spam.

In the physical world, someone can put a letter on your doorstep if they physically can make a letter and drop it off. Similarly, anyone with an iMessage/FaceTime account can enter any address and press send. Apple will deliver that message to you if your account is listening to the address the sender placed.

In many cases, people have several addresses in iMessage, and merely sending a message to an email associated with your Apple ID doesn't compromise your phone number, password, location or any other details about you by the mere fact that a message was delivered.

It's hard to tell whether the person has any information other than your email address, because it's probable they just guessed it. Email spammers use computers to generate millions of possible email addresses, and hope that some of them work. Also, the world is large, there could be thousands of people whose parents named them (or they chose an identity) the same as your fictional creation. Without engaging the sender or additional sleuthing, you may not be able to tell if this is a prank, intentional marketing for One Direction or a coincidence.