Eh honestly you don't legally need to inform KKH one, but as a courtesy it's better to let them know so they can free up the appointment slot for other mummies who need it lah! Just call KKH and cancel your future appointments, then proceed with SGH as private patient under Dr Yang, no need to make it so complicated. But hor, just be prepared that going private at SGH will be quite a big difference in cost compared to subsidised at KKH, so make sure you check your Medisave and insurance coverage first before you commit!