Miklagarðr, the Big City, was Constantinople, the capital of the Byzantine Empire. In Old Norse the Empire was generally known as “Grikkland”, which seems like it might have been a politically sensitive name since the Byzantine Emperors always called their Empire “Rome” and themselves “Roman Emperors”. But the Norse borrowed the terms used by the Germans and Slavic peoples who lived between them and the Byzantine Empire, and the Germans and Slavs primarily knew them as a Greek-speaking empire, so that’s the name they used.

During the crusades the Byzantines often came into conflict with the Holy Roman Empire, where the emperor also claimed to be the true Roman Emperor - to the Holy Roman Emperor, the Byzantine emperor was the “Greek emperor” and to the Byzantine emperor, the Holy Roman Emperor was the “German emperor”. There were lots of Vikings in Constantinople and elsewhere in the Byzantine Empire (where they were called Varangians), and some of them probably learned Greek, but it seems unlikely that the Byzantine emperor ever learned any Norse. The emperor probably didn’t know or care what the Varangians called him. Clever Norse-Greek interpreters presumably translated his title correctly!

Vikings were also familiar with the actual “Rom”, the city of Rome, which was in “Langbarðaland”, the land of the Lombards in Italy. The people inhabiting Grikkland were, of course, Grikkir.

Serkland was the name for Arab territories…probably. If so, then it must come from the same source as the Latin and Greek “Saracen”, which may be from an Arabic word “sharkiyun”. That word might mean “easterner” but it’s also not entirely clear what it means or if it’s even the origin of the word “Saracen”. The Medieval Latin understanding of “Saracen” was that it referred to the descendants of Sarah (and Abraham) in the Bible, or because they were “Syriginae”, inhabitants of Syria.

So, Serkland could also refer to Syria (otherwise known as Syrland). It could describe any place that was inhabited by Muslims, including North Africa (Affrika) and sometimes Sicily (Sikiley, which conveniently happens to contain -ey, the Old Norse word for island). Another possibility is that it has nothing to do with Saracens, but refers to Sarkel, a city in in Khazaria, or maybe the word for “silk”, referring to silk trade from Central Asia. Whatever it refers to, the people who lived there were the Serkir.

As for the Khazars, I don’t see any particular name for them or their territory, which seems strange since the Khazars were a significant neighbour of the Varangians. But they did have a name for the related Bulgars - not much different, it was simply “Bolgar”.

Norse literature and inscriptions are full of place names, and the list would be endless if I included them all here. In England lived the Englar, the Skotar live in Skotland; apparently there was no name for Ireland or Wales but the Irar and Bretar lived there. I always thought it was fun that the Viking name for the city of Nantes in France (Frakkland) was Namborg, and when Scandinavians visited crusader Jerusalem they called it Jorsalaborg.

Sources, for these names and plenty others:

Judith Jesch, Ships and Men in the Late Viking Age: The Vocabulary of Runic Inscriptions and Skaldic Verse (Boydell, 2001)

Sverrir Jakobsson, The Varangians (Palgrave Macmillan, 2020)

Sigfus Blondal, The Varangians of Byzantium, trans. Benedikt Benedikz (Cambridge University Press, 1978)

Krijnie Ciggaar, “Visitors from North-Western Europe to Byzantium”, in Mary Whitby, ed., Byzantines and Crusaders in Non-Greek Sources, 1025-1204 (Oxford University Press, 2007)

John Tolan, Saracens: Islam in the Medieval European Imagination (Columbia University Press, 2002)