A similarity transformation is introduced to reduce the generalized two-dimensional (2D) nonlinear Schrödinger (NLS) equation with modulated spatial coefficients and a special external potential to the standard NLS equation with constant coefficients. The 2D rogue wave solutions are constructed with the help of Whittaker functions in polar coordinates. We present some typical examples of the obtained solutions by selecting the two free parameters: the azimuthal number (the topological charge) and the radial node. With the help of two free parameters, the unique properties of solutions are discussed. Furthermore, we find that the rogue waves display different intensity patterns, such as the circular-pyramid, annular-ring and vortex-ring patterns.