Speaking of that... The name Sweden and it's variants (Sverige/Schweden/Suecia etc) goes back on the same etymological root as the third person reflexive pronoun "sig", with the meaning "one's own kin, ourselves". It's not all too uncommon to refer to oneselves as just "people". :)
I've also noticed that the three Finnish related languages in Scandinavia (Finnish "Ruotsi", Estonian "Rootsi", and Sami "Ruoŧŧa") are similar ... ultimate origin is proto-indo european word which means "Rowing". So in these languages, Sweden's name refers to a country where people like to row, perhaps a reference to the Vikings who first came to these countries in rowboats.
Another interesting tidbit: The Swedish word "sax" (scissors) may also come from this root. The word "seax" in Proto-German was used to refer to a variety of long knives which the Saxon tribe used, and is likely where the tribe got its name.
Also of note is the Scottish word "Sassenach" which they used to refer to English-speaking people, and likely also comes from this root.
This one is the real mystery. In Latvian, it's "Vācija". A few other minority languages (including "vakja" in Sami) are similar. It's thought that this was the word the Baltic people used to refer to Vikings. The name may have originated from a 6th century Swedish tribe called Vagoths. It's been theorized that the origin is an Indo-European word "wek" ("speak"), and also the root of the Latvian word "vēkšķis". If true, it's yet another reference to the foreign language of the German tribes which would have been incomprehensible to the Baltic peoples.
Here is a Wiki that explains the whole thing! It seems that there are 6 major root words for the names of Germany in various languages. Deutsch, German, Alemani, Saxon, Niemcy, and Vācija (Latvian) ... the last one seems to be related to a similar word in Lithuanian, but the origin is unclear. Alemani was the name of a southern German tribe in what is today Alsace-Lorraine, and likely the term meant "all men" or "foreign". https://en.wikipedia.org/wiki/Names_of_Germany