iPhone 7 Plus, Access to Messages I have a new iPhone 7 plus, purchased last week on my personal Verizon account. I have dialed and received calls and messages from only 1 phone number. I do not have an Apple ID or email or anything else setup on this phone. 

How would I receive a text message from an unknown number, which would indicate that this person could read my texts?
It appears you simply received spam. This, in itself, does not mean that this person has been reading your text messages. In fact they might have simply sent a generic message to random numbers, and one of them happened to be yours.

So unless that spam text referred to things you’ve said in private conversations, the spammer is NOT reading your texts. You are safe to delete the spam message by swiping left from your list of messages and tapping Delete.

If you want to go the extra mile, long-press that spam message. When the menu appears, tap More… followed by the arrow in the bottom-right corner of your screen. Forward that message verbatim to 7726, which is the number for reporting spam texts in the US. Verizon will then ask you for the number that sent you the spam. Respond with it and they’ll take care of it.