Ion cyclotron resonance heating (ICRH) has the potential of providing efficient ion heating of reactor grade fusion plasmas especially during the start-up phase. In order to assess such heating scenarios, ICRH modelling is required. However, the physics is complex and certain elements are not universally taken into account in ICRH modelling. In this paper we discuss the importance of including Doppler shift displacements of resonance points away from the cold resonance (i.e. where ω = n Ω c ) in Fokker-Planck calculations of the distribution function of resonating ions. In particular, the resonant interaction time and the wave electric field varies with the local Doppler shifted resonance positions. The importance of accounting for these variations in Fokker-Planck modelling is investigated. Furthermore, it is shown how these effects can be included in a simplified Fokker-Planck treatment that is sufficiently quick for integrated modelling frameworks of fusion plasmas. Because 2D effects in velocity space play a crucial role in determining Doppler shifts, we employ a model of the anisotropy of the non-thermal distribution function. Simulation results show that taking the Doppler effects into account in Fokker-Planck modelling can have a significant impact on the distribution functions of fast ions and important quantities, such as the collisional power transfer to the background plasma. This is especially important in cases where the poloidal variation of the left-hand component of the wave electric field is strong.