Have a look at "If Found" or "Return Me" in the AppStore.

Both are free and work well. You save the details as a screenshot photo, and then use the image as the screen saver when you turn on the phone. The password/fingerprint options work to keep everything secure with the screen readable if the phone is found.

I have used both happily and use Return Me at the moment on my 5s. On the screen it has my name, it has a phone number and an email address. It works as an ICE, and an "if found" contact.

If you have a problem with getting the image (which is pretty simple!), then pm me