Recently I got spammed via text message onto my cell phone and I am charged for it on my phone bill. Could I charge someone for this? Would it be considered harrassment? Even though the person mistakenly thought I was someone else. I told him to stop and he did.
That depends on state law. And I doubt that ANY state will consider one message "harassment".
I suppose you can always take the person to small claims court for the cost of any text messages to your bill, but it sounds as if they acted reasonably when you asked them to stop so I doubt there is any serious action you can take aside from asking for them to pay that portion of your bill.