Is the shape of your belly button dependent on how the doctor cuts the cord or is it like a gene thing?

Predetermined: Belly button shape ("innie" vs. "outie," for example) is all predetermined. It has nothing to do with cutting the cord.

Healing Process: The shape of your belly button (umbilicus) is not determined by how the cord was cut. However, the healing process largely influences the final outcome, such as depth, and coloration. Congenital anomalies of the umbilicus do occur: Meckel's Diverticulum, an intestinal pouch can extend into the navel, is associated with abdominal pain, blood in stools. Have your doctor check if further concerns.

It's up to you: The appearance of your belly button (innie, outie, round, oval, whatever) has little to do with how your umbilical cord was cut. The location of the cut and subsequent clamping does not involve the skin of the belly button. The fatty, muscle, and fascial tissues below the skin affect the shape of the belly button - so to some extent genes do have an effect.