You can add a message to Lost Mode, informing 'honest finders' of how to contact you. See - iCloud: Use Lost Mode
It's also possible to add text to your lock screen [We have that on both my & my partner's lock screen images, just in case either of us walks under a bus... which of course would not be a 'lost mode' situation]
I've been trying to Google some ideal lock screen info - but they all seem to be based on apps... all you really need is to know the screen size of your current lock screen image, add the text in Photoshop or Gimp etc & set as your new lock screen :/
This gives a decent general overview of how to change your lockscreen, but what you really need are the sizes, so you can make one with the '3D' view or just static - this page has a guide to image sizes [ignore that they're trying to sell you an app to do it, any image editor can do this].
This is my lock-screen...