So as you might know, the
National Romanticism came to prominence in Russia in 1800s as a result of the Napoleonic Wars. Since these types of movements revered the local folk culture and traditions, some people in Russia took the idea to its natural conclusion and called for removal of "foreign" reforms like those introduced by Peter the Great.
So I'm wondering: since the term "Russian Empire" was 1st made official by Peter the Great, was there any calls to rename Russia back to "Grand Duchy of Muscovy"?
No. It was primarily foreigners who referred to Russia as "Muscovy" and they did it largely to disparage the state, in the sense of emphasizing that it did not include all of the Rus' lands.
"According to prominent
historians like
Alexander Zimin and
Anna Khoroshkevich, the continuous use of the term
Moscovia was a result of traditional habit and the need to distinguish between the Muscovite and the Lithuanian part of the Rus', as well as of the political interests of the
Polish-Lithuanian Commonwealth, which competed with Moscow for the western regions of the Rus'. Due to the propaganda of the Commonwealth,
[35][36] as well as of the
Jesuits, the term
Moscovia was used instead of Russia in many parts of Europe where prior to the reign of Peter the Great there was a lack of direct knowledge of the country. In
Northern Europe and at the court of the
Holy Roman Empire, however, the country was known under its own name,
Russia or
Rossia.
[37] Sigismund von Herberstein, ambassador of the
Holy Roman Emperor in Russia, used both
Russia and
Moscovia in his work on the Russian tsardom and noted: "The majority believes that Russia is a changed name of
Roxolania. Muscovites ("Russians" in the German version) refute this, saying that their country was originally called Russia (Rosseia)".
[38] Pointing to the difference between Latin and Russian names,
French captain
Jacques Margeret, who served in Russia and left a detailed description of
L’Empire de Russie of the early 17th century that was presented to King
Henry IV, stated that foreigners make "a mistake when they call them Muscovites and not Russians. When they are asked what nation they are, they respond 'Russac', which means 'Russians', and when they are asked what place they are from, the answer is Moscow, Vologda, Ryasan and other cities".
[39] The closest analogue of the Latin term
Moscovia in Russia was “Tsardom of Moscow”, or “Moscow Tsardom” (Московское царство), which was used along with the name "Russia",
[40][41] sometimes in one sentence..."
https://en.wikipedia.org/wiki/Tsardom_of_Russia#Name