Some of the names derive clearly from former names of germanic tribes. For example the french and spanish names for germany clearly come from the "Alemanen" a tribal confederacy which occupied what is today Baden-Wuerttemberg and Alsace during the late antique and early middle age. When this name for a germanic tribe became the name for all the people of what is today germany i dont know.

Deutschland and Tyskland seem to derive from the self labelling of the germanic tribes. They seemed to have called themselfs "diutisc" meaning "belonging to the people".

Germany, German etc. derives clearly from the latin name given by the romans "Germanen". Its origin and original meaning is unclear.

For Nations without a border or any clear contact to germany it seems most plausible that they derived the name from the language which they heard the name the most or first time or taking the name of the german tribe (or people of the part of germany) they encountered.

Wolfgang Krischke: Was heißt hier Deutsch? Kleine Geschichte der deutschen Sprache.

Werner Besch u.a. (Hrsg.): Sprachgeschichte. Ein Handbuch zur Geschichte der deutschen Sprache und ihrer Erforschung. Band 3

Just a recommendation to ask in r/linguistics. Based on the question, their expertise might better serve you.

The historical region we now know as Germany was, for most of its history a collection of loose tribes and states that shared a a common heritage, a similar language, and, nominally throughout the Middle Ages and the Modern Era, a common sovereign. So the way people referred to the region was not commonly by the name of the whole region but instead by the name of the tribe or state you were most likely to interact with. The various names used today are either historical or semantic calques of the name the Germans themselves refer to the region. So Germany is a loanword from the region's historical name in Latin, Germania, which is itself a loanword from the Celtic language Gaulish; Deutchland (originally Teutchland) means “Land of the Teutons”, the Teutons being one of the many tribes that inhabited the region since Ancient Roman times (though, as it is usually the case, the word itself ultimately just came from the PIE word for “people”); Tyskland is the semantic calque of Teutchland, where Tysk is a cognate of Teuton; Allemagne (and, as mentioned in another post, Alemania) is a loanword from the name of a historical region, Alamannia, inhabited by another Germanic tribe in Ancient Roman times, the Alemanni; Vokietija is a compound word in Lithuanian meaning “land of the Vokietis”, the Vokietis apparently having been an ancient Swedish tribe that neighboured the Baltic states.

tl:dr Many tribes inhabiting the same region, so depending on which tribe you were the most likely to get raided by closest to, that was the name of the region.

Slavic names (e.g. Polish Niemcy, BCS Nemačka) are based on an old root *něm-, whose descendants in modern Slavic languages generally means 'mute', but which originally meant something more like 'having unclear speech'.

To expand a bit on this: it follows a trend in Indo-European languages where words or phrases related to clear speech are repurposed as names for a group's own language (or vice-versa) and words or phrases related to unclear speech, mumbling, or speech impediments are repurposed as names for the language of foreigners (the following will borrow from a conference handout). We have, for instance, Greek barbaros 'unintelligible, non-Greek', Sanskrit barbara- 'stammering', Latin balbus 'stammering', Serbian brboljiti 'chatter'--all of these can be related to a PIE form *barbaro, containing the rare-for-PIE sounds *b and *a. We see this implicit ideology also in the etymology of shqip 'Albanian' (and the verb shqiptoj 'to enunciate') ultimately from Latin excipare 'to take out [meaning]'. There's a phrase in Modern Greek katalavénis roméika, with the meaning of 'don't you understand plain language' that uses the language's autonym, romeika and links it with intelligibility. In Macedonian the typical linguistic autonym is nas 'our [language]'--you also see the forms po-našinski and po-naše (the same, but adverbs)--this usage is also seen in Bulgarian, BCS, and Russian.