If you were to write it in katakana you'd get pretty much the same! シャノン - Shanon. It's very forgiving to the Japanese alphabets. You could add another n in there (the only "lone" consonant in Japanese) to add emphasis on the double n in your name and get シャンノン, but that looks a bit unwieldy and unnecessary imho.
When my sis went to China she was told to get a Chinese name for convenience's sake, but in Japan you just try to get the sound as close as possible, written in katakana, which is the alphabet used for foreign words and names. (I went to Japan for one year, my sis to China haha).
