In the early nineteen fifties the Gibson Guitar Corporation wanted to market a solid body guitar under the name of a popular artist. Les Paul was the biggest electric guitar player at the time and had made his own solid body guitar which was the inspiration for the solid body guitar built by Leo Fender. Gibson wanted the prestige of building a guitar under Les Paul's name. The Gibson company designed the guitar and submitted it to Les Paul for his opinion. He suggested some changes to the way the guitar looked, the company made the changes and they named the guitar after Les Paul. You can find an article on the subject at Les Paul Guitars - What Makes Them Special?