It is very difficult to know what sorts of actions could be taken to deter identity theft. We are generally not very good at deterring crime of any sort. Therefore, it will be very difficult for us to deter identity theft.
One way to deter identity theft is to make it much harder to do. This might be possible if internet commerce sites were to take very strong measures to protect their data from hackers. This is, of course, more easily said than done since hackers are very skilled at breaking into computer networks and stealing data.
Another possibility is to make the punishments for identity theft so draconian as to scare people from committing the crime. However, this too has its problems. First, it is not at all easy to catch people engaged in identity theft. This makes it harder to deter them with harsh punishments. Second, it is not certain that we would be willing to impose harsher penalties on identity theft than we do, for example, on physical assaults.
Thus, there are things we could do to deter identity theft, but it is not at all clear that these actions would work.
Harsher punishments for those convicted.