from www.swingstreet.com:

The very first known form of swing was the Texas Tommy in 1913, which later changed to the Mooch and Sugar in 1916 and even later called the Break-A-Way by 1919. During the 1920's when the Charleston was becoming all the rage, the Breakaway and Charleston would start to mix with and was forming a new yet unnamed dance style with a few other dances thrown in the mix.

--- In 1927 this style was finally acknowledged and given a name by a fabulous swing dancer named George "Shorty" Snowden. 'Shorty George' from New York's Harlem was to re-name the 'break-a-way' the "Lindy Hop or Lindbergh hop" after the famous pilot "Charles Augustus Lindbergh" (Lindbergh made his thirty-three hour flight across the Atlantic Ocean to France successfully on May 20, 1927.) There are two main stories about the name that go something like this (the 1st one being the main one):

Order 'Swing Kids' click here
--- 1) In September, 1927, a newspaper reporter having never seen this style of dance before walked up to the winners at a dance marathon contest in Central Park in New York, (known as the un-official start of the Harvest Moon Ball Contest (later to be tried again in 1934). This reporter asked the winning couple (Shorty George!) what it was that they were doing, as he had not seen it before. Shorty thought for a second and replied "the Lindy Hop... We flying just like Lindy did!". The newspaper reporter did an article on the contest in his newspaper and described what he saw calling it the "Lindy Hop."

--- 2) A dance derby (marathon) which started on 6/17/1928 at the Manahattan Casino, (155th Street and Eighth Avenue in Harlem, New York.) Shorty George (#7) was Dancing in a (supposedly non segregated) dance marathon and decided to do the Breakaway, a reporter for the New York Graphic (?Walter Winchell maybe?) observed and came over and asked what kind of dance he was doing, Snowden without stopping, thinking quickly replied "The Lindy Hop... Were flyin' just like Lindy did!"... supposedly he reported this in his article. Fox Movietone News also captured Shorty's feet in this derby on film. Shorty became one of the remaining four couples out of eighty left dancing before the marathon was closed down on 7/4/1928. The New York Times announced: "NEGRO DANCE DERBY ENDS.; Stopped After Sixteen Days by Order of Commissioner Harris." However there are publications that use the term Lindy Hop prior to this date, so number one is probably closer to the correct story.

--- In the last 90 years the Lindy has become the first form of swing as we know it today (the Great Grandfather of all Swing if you will) and along with the Charleston were the main dances of the 1920's. The Charleston mixed in with the Lindy, as well as other prior forms of dance such as the Texas Tommy, Turkey Trot, Apache Dance, Black Bottom, The Shimmy, The Strut, Cakewalk, The Frisco, Foxtrot, Tap and more. These dances were known as "Jazz Dances." The Lindy was the first form of swing "White America" had seen and was about to fall in love. Some of these folks would go to the famous "Savoy Ballroom" in Harlem and watch the "African-American dancers" strut their stuff.