You are confused about the sampling rate and the ADC rate.
The registers you refer to in the manual only control the taking of one sample. The registers allow you to control how long to sample the voltage for. This may make a difference to you depending on the circuitry involved. That is, you don't want to take the sample too fast for your circuit. (I didn't look closely at the datasheet, but some microcontrollers take several samples and average them. This behaviour is controlled by registers, too.)
But the 8 kHz sampling rate refers to how often you want to sample. That is, this is the frequency you want to trigger the individual samples. The registers you mention don't address this. You need to use a clock and an interrupt handler to move the data out of the register into storage somewhere or do something with it, and then trigger the next sample. There is also an interrupt handler that can deal with the sample as soon as it is ready. In that scheme, you use to handlers: one to trigger the samples; another to deal with the samples when they are ready.
Edit:
To explain more why you don't want such a slow ADC rate, consider how the ADC generates its data. It samples for the first bit, waits a cycle, samples for the second bit, and so on for 10 cycles. The accuracy of the result depends on the signal staying stable over all these samples. If the signal is changing, then the bits of this number are meaningless. You need to set the prescalar and ADC clock fast enough so the signal does not change, but slow enough for the signal to settle.
So yes, you want to use a clock and interrupt handler to read the data then trigger the next reading. The ADC runs independently of the processor, and will be ready by the time the interrupt runs again. (The first reading will be garbage, but you can set a flag or something to guard against that.)
volatile int running = false
Handler()
if(running) do something with data
running = true
trigger ADC
output compare += 1/8000 s