There is a large body of evidence showing that the existence of a suitably-constrained derivation on a 3-prime near-ring forces the near-ring to be a commutative ring. In the present paper, we investigate the notion of left generalized derivation satisfying certain algebraic identities in 3-prime near-ring N which forces N to be a noncommutative ring. Moreover, an example proving the necessity of the primeness of N is given.