When people receive emails which appear to come from their own address but they haven't sent (or bounces of messages that appear to come from their address) they naturally tend to be concerned: however it's most unlikely that anyone has hacked their account, they've just been targeted by one of two common spammers' techniques: both arise because it's all too easy to forge the 'from' address on messages to be something other than the real one.
There are two things that can happen. One is that the sender has forged the 'from' address to be the same as the 'to' address (so other people will see it coming from themselves, not you), presumably in the hope of confusing spam filters. It's harmless, if extremely annoying. Delete it (never ever answer spam or try to unsubscribe from it), and you don't need to be worried about it.
The other problem, which is apparently the one affecting you, is that a spammer is forging your address as the 'from' address on a whole batch of messages. The first thing you hear about this is when you start getting bounce messages because the spam has been sent to non-existent addresses and is being bounced to you. There's no point at all in responding to it. It's infuriating but normally stops after a bit as they move on to another forged address.
As its unlikely to be a case of your account being hacked and used to send the messages there isn't really anything you can do about it: closing the account isn't really worth the hassle unless you are totally swamped, because you will have to tell everyone your new address. Apple can't really do any more than they already are about spam.
If you really want to abandon the present iCloud account just sign out of it on all your devices and forget about it: you can't delete it from the server, but it will just collect email until it's full and then bounce them with an 'account over limit' error.