How did the genre Jazz, get the name "Jazz"?

New Orleans and NOLA's culture is responsible for the creation of jazz and the word. It's a mixture French, Spanish and Creole words. To translate it means "I am feeling it."

hum hum oh the mom named him/her

you can look it up on wikipedia

the American Dialect Society:
There is no definitive etymology for jazz. However, the similarity in meaning of the earliest jazz citations to jasm, a now-obsolete slang term meaning spirit, energy, vigor and dated to 1860.
Jazz began as a West Coast slang term around 1912, the meaning of which varied but which did not refer to music or sex. Jazz came to mean jazz music in Chicago around 1915. Jazz was played in New Orleans prior to that time but was not called jazz.
Read more: wikipedia

Here is a fine link to the PBS website on Ken Burns' Jazz. I do recall when I watch it that the phrase was originally termed "Jass" but modified into the word Jazz.

even if there is a kernel of truth to it, do not fully trust anything that Ken Burns has to say about the history of jazz, for it is merely the greatly-abridged history of jazz according to Wynton Marsalis that he is promulgating/regurgitating. see the link below for both an excellent interview with Archie Shepp that serves to, among other things, shed some light on the origins of the term "jazz."

A guy named jasmine peters.