If it is under your thumb, you notice it every time you are in that part of the neck, and it doesn't become a useful landmark that you actually take advantage of, then take it to the shop. Any DIY repair is going to leave you with a look you might not be happy with or a bump or other undesirable feeling under your thumb potentially worse than what you are dealing with now unless you absolutely nail the repair and make it perfectly flush. Our hands can feel incredibly small deviations in texture and to eliminate that you would have to fill it in, smooth it flush, and then refinish the surrounding area. If it bothers you and you don't want to ever notice it's there, professional help is your best option.
If it isn't under your thumb and the only issue is cosmetics, crack open a walnut, and rub it on the spot. The oils in the nut will darken it so it doesn't look much different than the surrounding area without a texture change or weird colour contrast between the neck and whatever other type of finish you would be interested in. Total cost? 10 seconds of time, and a few cents for the walnut. Or you buy a bag of walnuts for a few dollars, fix the problem, and have a nice snack after you're done.