Shannon occurred sporadically as a boy's name in the 19th century in the United States. If you check the Social Security website, you will find that
Shannon was among the top thousand names for males in the single years of 1881, 1885, 1890, and 1904 while the first year it was among the top thousand names for girls was 1937.
I think it's unlikely that the use of
Shannon as a given name in the 19th century was a direct transfer from the name of the river, but instead was probably a use of the surname, which can be a variation of the more common Irish surnames Shanahan or Shinane, according to MacLysaght's
The Surnames of Ireland. Though the custom of using surnames as given names was until recently much more common for boys than girls, there have always been a few girls given such names since the start of the process back in Elizabethan times.