In modern English, Russia is used most often for naming Russia in all its forms through the time since the 8th century.

However, in Ukraine there is a strong trend to revise the Russian history and to force English-speaking world to use terms and stories elaborated by the Ukrainian nationalists, claiming that the mainstream English historiography reflects the imperial Russian point of view.

Please refer to History of Russia, Kievan Rus, Etymology of Rus and derivatives.

Here are some interesting facts:

• The first time Moscow referenced in 1147.
• The Moscow principality started to exist about 1300.
• Ivan III the Great officially used title "Ruler of all Rus" at least since 1493.
• Moski and Muscovites were used by Matvej Mehovski (he is considered to be a Pole) in 1517 (Tractate about two Sarmatias). (It's most probable that it was him who invented these words.)
• Ivan IV was inaugurated in 1547 as "Tsar of all Rus" (he was the first tsar in Russia).
• Sigismund von Herberstein published his "Rerum Moscoviticarum Commentarii" in 1549 (the word Muscovy was not widely used in the West before this book).
• Alexey I promoted the Greek form of Russia (Rossiya) at least since 1654, but probably before 1650.
• Russia and Ukraine (re)united in 1654.
• Peter I asked his ambassadors to request other governments to Russia instead of Muscovy since 1713.
• Peter I the great was inaugurated in 1721 as "Emperor of all Russia".
• Francishek Dukhinski (he is considered to be a Pole) started a propaganda that Muscovites are not Slavs since 1857 (Poles were preparing "antimuscovite" uprising in Ukraine).

Now the comments come:

• Considering that there are no known (at least to me) mentions of Muscovites before 1493, when Ivan III the Great started to use title "Ruler of all Rus" officially, it seems to be very plausible that "Muscovites" were invented in Poland-Lithuania in response to the Ivan III's claims to be the ruler of all Rus. The cause and the effect.
• It seems that the country was never called Muscovy by its inhabitants, neither officially, nor non-officially. All the rulers of the Moscow principality pretended to be more than just the Moscow rulers, and there always was a desire for pan-Russian rule. The people mostly called themselves Russian, some others used their tribal names, but they didn't name themselves Muscovites.