Recently my cell phone started telling me names of strangers who text me

This seems to have just started in the last month or so.  When I get a text from someone who isn't a contact yet, it's started showing me their full name at the top of the text.  If I go to make them a contact, I have to type in their name still.  I'm on an Android phone.  Is this a new thing for just me?  

Is there a way to make it so that your name doesn't show up on their phone when you text a new number?  I'm thinking about things like meeting someone to sell a lawnmower or to arrange a criminal enterprise...

I have had this happen on and off for maybe10 years now. It is far from consistent. The ID is often something like “Maybe Mary”. I am on Verizon.  Sometimes there is a last name attached.  This is for maybe one out of a hundred calls.

I have also had this happen on the flip side. Maybe 2 years ago I called a gentleman for the first time. He answered “ Hello John”.

Mine asked me if that number was that person lol a little creepy it's only happened once