Assuming, in the program, there is the function that provides on/off button on the screen. If OFF is selected, you cannot draw on it

Could this function be called "Rendering On/Off function"?

You can, but most people would not know what "rendering" means in this context.
Render has many very general meanings -- to give, to perform, to return, to furnish, to pay, to depict, to deliver, to melt down, to process and to translate -- but each is only valid in restricted circumstances.
I wouold call it the "drawing enabled / disabled" function. " Drawing On/Off" would probably work, too.
AlpheccaStars"drawing enabled / disabled" function. 
Thank you very much for your help!!! ApheccaStars!