"Muscovy" is an old name for the region of Russia surrounding Moscow, but these ducks neither are native there nor were introduced there before they became known in Western Europe.
It is not quite clear how the term came about; it very likely originated between 1550 and 1600, but did not become widespread until somewhat later.

In one suggestion, it has been claimed that the Company of Merchant Adventurers to New Lands traded these ducks to Europe occasionally after 1550; this chartered company became eventually known as the "Muscovy Company" or "Muscovite Company" so the ducks might thus have come to be called "Muscovite ducks" or "Muscovy ducks" in keeping with the common practice of attaching the importer's name to the products they sold.
But while the Muscovite Company initiated vigorous trade with Russia, they hardly, if at all, traded produce from the Americas; thus they are unlikely to have traded C. moschata to a significant extent.

Alternatively—just as in the "turkey" (which is also from America, not Turkey), or the "guineafowl" (which are not limited to Guinea)—"Muscovy" might be simply a generic term for an exotic place, in reference to the singular appearance of these birds.
This is evidenced by other names suggesting the species came from lands where it is not actually native, but from where much "outlandish" produce was imported at that time (see below).

Yet another view—not incompatible with either of those discussed above—connects the species with the Muisca, a Native American nation in today's Colombia.
The duck is native to these lands too, and it is likely that it was kept by the Muisca as a domestic animal to some extent.
It is conceivable that a term like "Muisca duck", hard to comprehend for the average European of those times, would be corrupted into something more familiar.
Likewise, the Miskito Indians of the Miskito Coast in Nicaragua and Honduras heavily relied on it as a domestic species, and the ducks as well may have been named after this region.
"Muscovy" is an old name for the region of Russia surrounding Moscow, but these ducks neither are native there nor were introduced there before they became known in Western Europe. It is not quite clear how the term came about; it very likely originated between 1550 and 1600, but did not become widespread until somewhat later.
In one suggestion, it has been claimed that the Company of Merchant Adventurers to New Lands traded these ducks to Europe occasionally after 1550; this chartered company became eventually known as the "Muscovy Company" or "Muscovite Company" so the ducks might thus have come to be called "Muscovite ducks" or "Muscovy ducks" in keeping with the common practice of attaching the importer's name to the products they sold. But while the Muscovite Company initiated vigorous trade with Russia, they hardly, if at all, traded produce from the Americas; thus they are unlikely to have traded C. moschata to a significant extent.
Alternatively—just as in the "turkey" (which is also from America, not Turkey), or the "guineafowl" (which are not limited to Guinea)—"Muscovy" might be simply a generic term for an exotic place, in reference to the singular appearance of these birds. This is evidenced by other names suggesting the species came from lands where it is not actually native, but from where much "outlandish" produce was imported at that time (see below).
Yet another view—not incompatible with either of those discussed above—connects the species with the Muisca, a Native American nation in today's Colombia. The duck is native to these lands too, and it is likely that it was kept by the Muisca as a domestic animal to some extent. It is conceivable that a term like "Muisca duck", hard to comprehend for the average European of those times, would be corrupted into something more familiar. Likewise, the Miskito Indians of the Miskito Coast in Nicaragua and Honduras heavily relied on it as a domestic species, and the ducks as well may have been named after this region.
Muscovy duck