While there are those who believe that perhaps the Phoenicians discovered the New World, I don't think anyone thinks they came up with the name America. Yet perhaps, just perhaps, there might be a Semitic connection to the name.
Many years ago, I wrote to the columnist Cecil Adams:
We all know that America was named for Amerigo Vespucci. What does Amerigo mean in Italian?
He replied that:
Since you asked, there are a couple of theories on the name's origin. One is that it is a variant of Enrico, the Italian form of Henry, and derives from the Old German Haimirich (in later German Emmerich, in English Americus), from haimi, home, plus ric, power, ruler. Alternatively, it may come from the old German Amalricus, from amal, work, plus ric. (Amalricus the foreman? Beats me.)
Amal means work in Old German? It means the same in Hebrew! However, I have never been able to find any connection, or even an etymology of the German amal (perhaps to an earlier Indo-European root.) Maybe a reader knows or can find something out?
In any case, besides meaning "work, labor", the Hebrew word עמל amal, has a number of different meanings in many various locations in the Bible. Its meanings include: wealth, sin, suffering, trouble, oppression, mischief and pain. I have not found one unifying theory that explains all appearances of the word. It will often have different meanings in the same book. (See Robert Gordis, "On the Meaning of עמל in Koheleth" in Koheleth - The Man and His World, page 418).
In Arabic, the related words amil and amala mean "he did, acted". In Medieval Hebrew we first see the word amil עמיל - "agent, broker" from the Arabic. As far as I know, this word is not used much today, but in Modern Hebrew we find that the Arabic amala has been adopted into Hebrew - עמלה - as "commission, fee". This I hear all the time, especially at the bank...
Another derivative is ta'amula תעמולה - "propaganda". According to Klein, this word is also from the Arabic amil (business representative, agent.) Ta'amula has somewhat of a negative connotation, and therefore often it will be someone else's ta'amula, but your hasbara הסברה - "explanation, advocacy". That's what we need in America these days...