Does it hurt to have a tattoo on the side of your neck?

Short answer, yes, getting a needle covered with shoved into the skin of your neck thousands of time, a minute hurts.

Slightly longer and more informative answer, probably not as much as you think. At least not if it is comparable to the tattoos i have, The back of the neck is mostly skin over muscle, and the nerve density doesn't seem too high, it should be comparable to back tattoos or my scalp tattoos.