One of the great peculiarities among these names is the Turkish name for Greece, "Yunanistan". It's odd because it ultimately comes from the name of the region Ionia -- but Ionia is not in Greece: it's in Turkey.

but Ionia is not in Greece: it's in Turkey
But Ionia was largely Greek when the Turks (fairly recent arrivals in Turkey) arrived there. Because of their location, Ionians tended to be the first Greeks that people coming from the SE encountered. Arabic, Hebrew, Sanskrit and Persian all use similar names for Greece, so it is possible that the Turks already had the name before they got to Ionia.
Yes, there's a good reason for "Yunanistan", since there were Greeks in what is now western Turkey before the Turks were there. It's just looks odd.

A couple of examples from Polish:
Włochy (Italy, already mentioned above)
Węgry (Hungary)
Not, a country but a region - in Polish Siedmiogród, in German Siebenbürgen, Hungarian Erdély. To English speakers known as Transylvania.

OK, time's up for the quiz.
The country that the Estonians call Uus-Merema is
(Last chance -- don't look below)

New Zealand.
I would guess that Uus is new and that Meremaa is what the Estonians call the Danish island of Zealand -- although NZ is actually named for the Dutch province of Zeeland. But maybe Meremaa just means Sea-land (as both those names do), without reference to either the Danish or Dutch places, and it's a sort of translation.
I would guess that Uus is new and that Meremaa is what the Estonians call the Danish island of Zealand -- although NZ is actually named for the Dutch province of Zeeland. But maybe Meremaa just means Sea-land (as both those names do), without reference to either the Danish or Dutch places, and it's a sort of translation.
Interestingly, the first proposition fails the Wikipedia cross-reference test. In Estonian, Zeeland is Zeeland and Zealand is Sjælland. It looks like the second hypothesis is nearer the mark.
I like the fortuitous half translation, half phonetic transliteration of New Zealand into Chinese: 新西兰 "Xin Xi Lan" = New West Orchid.