Is it normal to have a stiff neck after a dumbbell bench press 3 reps session? I mean, I don't feel like moving my neck too much uptill some time after bench pressing. Is that normal?
Normal, no, but not uncommon. The most likely explanation is overuse of the trapezius muscle, whose origin traverses the external occipital protuberance and spinous processes of cervical (neck) vertebrae. Its function, among other things, is to elevate the shoulder girdle or, alternatively, stop its depression. In the bench press, it is primarily used to stabilise the joint during movement, and this is particularly important with dumbbells, since they inherently have more degrees of freedom than a barbell or machine, for example.
It is not uncommon to forcedly elevate the shoulders during the dumbbell bench press movement, and therefore to have excessive fatigue and muscular tension in the neck following a bout of exercise. This might be exacerbated if you have a shoulder injury causing greater instability, such as an acromioclavicular ligament tear. However, it can also simply be the result of sub-optimal exercise technique.
To limit the contribution of the trapezius muscle during the dumbbell bench press, the shoulders should be depressed throughout the movement, and the neck relaxed. Or, if you are performing an inclined press, at the bottom of the movement, elevating gradually as the dumbbells reach their peak, then returning to the depressed state at the bottom.
I hope that is helpful.