Yes Germany is very strange. They call their country 'Deutschland' , their natives 'Deutsche' . If I remember correctly, the French call Germany, 'Allemagne' . So, they have quite a lot of different unrelated names. They 've had a lot of changes the last 150 years or so, Prussian states to Germany to the Berlin Wall to reunification. It's a wonderful country now.
You're right! "Germany" has many different etymologic names in different languages. The adjective "deutsch" is related to "Teutonic" and to "tedesco" as well as to the English word "Dutch" which, however, refers to a different nationality. The Scandinavian languages use the "correct" word for Germany, for example "Tyskland". In Finish it's called "Saksa" which refers to "Saxonia", being is a part of Germany. There are more roots like "Alemania" or "Nemecka" which is used by many Slavic languages as well as Hungarian where it's "Németország".
There are even stranger names for Germany, but my favourite is in Navajo "Bééshbichʼahníí bikéyah".
You can find more about this here: https://en.wikipedia.org/wiki/Names_of_Germany
There is a legend about Germans. In my language (Croatian) we call the country Njemačka (in Croatian "nj" is one letter). But the people we call "nijemci" which is the word for the people who cannot speak = speechless, voiceless, mute. The legend says (or maybe it's the true story), that when Germans first came to this territories they couldn't understand what people were talking (which is normal, that you don't understand any language that you hear for the first time), so they kept silent. So others just called them NIJEMI (which turned into nijemci) = silent, mute...