There are interesting legends and a bit of lore about Mulek—his name and how he arrived on the American continent. The name "Melek" is the word for "king" in Hebrew. It is the opinion of some scholars that several passages in the Book of Mormon which reference the "king" should really be translated as "Mulek" and not "king." If that is so, we can learn a little bit more about who Mulek might have been. Apparently, Mulek was a son of King Zedekiah. After Lehi left Jerusalem, King Zedekiah, along with his other sons, were taken into captivity by the Babylonians and were killed. However, Mulek was able to slip away somehow. We do not know how he got to the New World. I like to think that Mulek and his guardians found passage on a Phoenician ship. The Phoenicians, at this time, were notorious for their ship-building and sailing skills.
Sidon and Tyre were two major shipping centers in Phoenicia, not far from Jerusalem. These two cities were intense competitors—even enemies. Individuals and nations would not normally have traded or engaged in business with both of these centers of commerce. One of the cities was a trading partner with Egypt and the other a partner with Babylon. Egypt and Babylonia were rival nations and generally were not on good terms, which created the tension between Sidon and Tyre. Lehi probably traded with one or the other of these large shipping centers.
Hugh Nibley pointed out that there may have been a connection between the name of the large river running through the land of Zarahemla and the old world of Jerusalem and Phoenicia. That river was named "Sidon"—the same name as one of two large shipping centers in Phoenicia.
If Mulek was transported to the New World on a ship run by the Phoenicians from Sidon, they may have chosen to name the prominent river in their new land after their place of origin. When the Nephite people of Mosiah met the Mulekites, the land was already called "Zarahemla," which is a Mulekite name. You would think that the primary river in the region would also be a Mulekite name—but it was not. This fact may be evidence of a Phoenician connection.
Book of Mormon Central, "Has An Artifact That Relates to the Book of Mormon Been Found? (Mosiah 25:2)," KnoWhy 103 (May 19, 2016).
Jeffrey R. Chadwick, "Has the Seal of Mulek Been Found?" Journal of Book of Mormon Studies 12, no. 2 (2003): 72–83, 117–18.