In Denmark, and soon to follow all over the EU, drone registration numbers including the owner name and phone number are to be clearly visible either on the top or sides of the drone, just like regular aircraft. If you join a hobby club that offers aircraft ID (like tail numbers on aircraft) that are supported by the local traffic authority, then you are required to display those too. Typically those are linked to the insurance offered by the club - but 'your mileage may vary'.
There is a big push to create UAV traffic management solutions - as the prediction that more and more commercial drone usage is going to happen in the future - so there are companies coming up with ways of using things like wifi and 4G mesh networks to determine UAV positions, and some sort of beacon (via software) may be required to be broadcast, giving the UAV details, just as in real aviation.
So expect changes around the world to make drone registration above a certain weight and class along with traffic management similar to aviation practices. I suspect this would mostly affect commercial pilots. Hobby flyers in your backyard or private farm in the middle of no-where would likely be unaffected.
Oh and by 'traffic management' I don't mean turning us into pilots with radios doing callouts for departure and arrival stuff. But the drone will at least broadcast an identity so that cities can track where it goes withing certain boundaries. Probably need to have flight plans registered somewhere too.
Currently here in Denmark, if I fly a job (photography, survery ,etc.) with anything above the weight of a toy racing drone, I have to file a flight plan with the local police 24 hours before the 'mission' - where I will be, how long is the flight, etc. I suspect this will become more automated over time.