THIS is the kind of thing that keeps me from getting the newest iOS version as soon as it comes out! I always give it a few weeks for Apple to work out the bugs - and/or respond to complaints and concerns. In this case, the new "Namedrop" feature has many police departments even issuing a warning!
Namedrop defaults to being automatically on when you install the latest iOS version, so you don't even know it's working in the background. Then, if your iPhone comes within close proximity of another iPhone, the two will automatically share contact information - again, without you knowing it. That could include your name, address, cell number, email address, social media handles...anything you've entered in your contact information. It does not however share any banking/financial information or passwords, etc. Still, in a world full of creepy people I'm sure you agree - we don't need others knowing how to contact us without our permission.
Here's how to disable it: