Swati.. under companies act 2013, the term "nominee director" is used only for the purpose of excluding such director from position of independent director.. ie., the context in which "nominee director" is used is with respect to independent director.. since private company is not covered under provisions of independent director, it really doesn't make difference to private company whether it designates a person as director as director or nominee director.. irrespective of such designation, his legal position remains same in that private company..
so, since private company is not covered under independent director's provisions and consequently concept of nominee director doesn't apply to it, it is advisable to use "director" only.. in the context of private company "nominee of shareholders" is a commercial position and not a legal one..