Place a hat or a small towel between your head and the plate. This will create padding between the plate and your skin which will prevent skin damage.
Watch your hands. You can use your arms as additional weight, but it always prefered to disengage them, as it much better to track the progress by increasing plate weight. Hands can interfere with this, since it is easy to help or complicate the exercise depending on the your hands position.
The key to neck training success is volume, never forget this.