Can bad posture be corrected to have a straight back and good neck position?
The simple answer is yes you can improve weak posture.
The long answer is that it is impossible to assess posture from this picture. the angle and the suit hide or accentuate things that may not be reality.
Let me first address proper strong posture. You don't want your back or neck straight when viewed from the side. The proper curve of the spine all the way down acts as a spring to absorb shock. If you are too straight or too curved then you will have weak or stress points in that spring. These areas will be most likely to be injured. Proper posture can help to prevent this problem.
Chiropractic can help you to find proper posture in standing and motion, but to keep these areas strong you must practice just like you do to keep any activity strong from sports to painting and everything in between.
To start with you will need an assessment to figure out what areas of your posture are weak. One of the most common areas is the neck as you asked about. Often this is referred to as tech neck from all the looking down that we do when we use technology such as phones or tablets or computers.
When you find the weakness you need to strengthen it. The biggest mistake people make when trying to improve their posture is forgetting to really strengthen postural muscles. They just sit up straight then after about 20 min they're back to slouching because their muscles cannot maintain it they are fatigued. I have some exercises that I've used for years to strengthen posture in my patients. Here are three simple ones, give them a try and see how your posture improves.
Shoulder Wall Slides (Muscle group: Lower Traps, Rhomboids, Scapular and Thoracic Spine Stabilizers)