What are the modern names of Magog and Gog? Are these countries or cities?

Well, most of the time they are people.

There are uses of the words to indicate that they are geographical regions but the evidence for where those regions were sited is vague and the interpretation disputed.

The possible regions include Egypt, Babylon, Lydia (modern-day Turkish provinces of Manisa and Izmir), Asia Minor (most of modern-day Turkey) in general and Scythia (land to the north of the Black Sea) by Josephus, Unfortunately "Scythia" is often used to mean "somewhere vague up North" so that's no help.