I've been searching on internet for this for a long time.
What is the name of material which is transparent, elastic and it sticks to plastic? Something that is used to cover back and front of mobile phones to protect them.
If you mean the film for temporary protection of the display windows, I have always assumed it is flexible vinyl (plasticized PVC). There are probably several different materials used.
Some of the many types of films available for glass that do all sorts of things. I would contact 3M with your specific requirements
There are many suppliers of such films.