Turkish, Arabic, Spanish for "Germany" are obviously cognate. But not with "Germany" or Deutschland.
At least two of them must be borrowed. Which, and what is the (commonly assumed) source?
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Spanish Alemaña (as well as French Allemagne and Portuguese Alemanha) derives from Latin Alemannia, which in turn comes from Alemanni, which was a confederation of German tribes. The Online Etymological dictionary says this comes from Proto-Germanic Alamanniz, which possibly meant "all men" (which makes sence, since they were a confederation); an alternative would be "other men", from Latin alius and Proto-Germanic manniz.
It could also be that the Spanish word is a borrowing from French, as it was among the Franks that Allemand first became a term for all "Germans". In this case the etymology of the Spanish word would be more complicated: Proto-Germanic -> Latin -> Frankish -> Old French -> Spanish.
The Arabic word must have been borrowed from Spanish, and the Turkish word would then be a borrowing from Arabic.
To take into account the comments below, Spanish Alemaña derives from Latin Alemannia, either through Frankish -> Old French -> Spanish or through Frankish -> Iberian Romance -> Spanish. The Arabic word must be a borrowing from Iberian Romance or Spanish (because a literate borrowing from Latin would result in word similar to Germania, which was the Classic Latin most common name for the region and its people), and the Turkish word must be a borrowing from Arabic (because if they acquired the word via Eastern Europe instead, they would most likely borrow from either German Deustcheland, Greek Γερμανία, or some slavic language, in which case it would ressemble something like Njemačka).