A person who solves jigsaw puzzles is commonly referred to as a "puzzle solver" or a "jigsaw puzzler".
There is no specific personality traits that are associated with someone who likes puzzles, as people from different backgrounds and with diverse personalities can enjoy solving puzzles. However, people who enjoy puzzles tend to be patient, persistent, and have a desire to solve problems. They are also known to be detail-oriented, analytical, and good at recognizing patterns.
Some people may be naturally good at jigsaw puzzles due to their cognitive abilities such as spatial awareness, pattern recognition, and memory recall. They may also have a strong attention to detail and a good sense of spatial relationships. Additionally, some people may also have developed their skills and abilities through practice and experience in solving puzzles.
There is no specific term for a person addicted to puzzles, but some people may develop an excessive interest in solving puzzles, to the point where it interferes with their daily life. This kind of behavior is classified as "compulsive puzzle-solving" and it could be part of obsessive-compulsive disorder (OCD) or a compulsive disorder. However, it's important to note that for most people, solving puzzles is a healthy hobby and not considered as addiction.