In the second chapter of the Book of Alma, within the Book of Mormon, seditionists wage war atop the hill Amnihu, east of the river Sidon, near the capital city of the Nephites.
The Biblical King David had a son, Amnon, which according to Strong's Concordance can be transliterated Aminon, but I think the etymology of this place derives from another Biblical word ... Near Damascus in the Holy Land is the hill Amanah, which is Hebrew for "faithful."
Yet another amazing cooincidence for the imaginative Joseph Smith, or a neat little mark of authenticity? You decide.
What of the river Sidon? Why would Nephites, expatriate Hebrews, name their principal New World river for that Phoenician -- foreign -- city?
Perhaps they did for the same reasons the United States has a Paris, Moscow, Memphis, Philadephia, New London, etc.
Or perhaps it is because Sidon is Hebrew for "fishery." Which could be expected to be a major business upon a major river. Old World Sidon may not have come to their minds at all.
Typically, the New Testament has Sidon while the Old has Zidon -- both of course translating the same word which in Hebrew begins with the letter "tsadee," pronounced "ts," which is neither an s or a z but a little of both. Hence the difficulty. We see this with other words such as Melchizedek (OT) and Melchisedec (NT).
But Sidon appearing in the Book of Mormon is hardly an anachronism. If you are still not convinced, Genesis 10:15 should put your mind at ease.