I was just wondering if it is possible to access prefab names from a script. For example if I have a Transform variable and I set its value to a prefab named "Arrow" from inspector, then would it be possible for me to get that same string "Arrow" in the script?
If you are refering to the name then yes. http://unity3d.com/support/documentation/ScriptReference/Object-name.html
Yea, you can access everything from prefabs, including .name. You have to be a little careful on modifying variables of a prefab as most of the time they will be saved. Just keep in mind that Awake / Start does not get called on prefabs, just their instances. So if you need to run some code from a prefab's script you've got to use OnEnable or OnDisable