What is the name of the technique in which a photo is "simplified" by reducing the complexity of the colors in it?

This can be called decrease in color depth, reducing the depth of the bit or reducing the number of color planes (for bitmaps, in particular). GIF images, for example, can have only 8-bit color (256 levels), "JPEG 2000 supports any bit depth, such as 16-bit and 32-bit floating-point pixel images." The decrease in color depth, taken to the extreme, produces poster-type images, which can show bands where the colors had gradations.

To reduce the depth of color, try a tool such as the free IrfanView, shown below. In addition, gray scale conversion effectively eliminates everyone Color information: only a single channel is used.

IrfanView decrease the color depth