"Slav" deriving from the Slavic term for "word" is something of a false etymology that was invented in the 19th century. It is implausible on philological grounds: you'd expect a different vowel in this word if this were the case, and the suffix *-ninъ is only otherwise used in terms derived from place names.

It is more likely[0] that the term derives from some toponym. This is in line with how tribal names tend to work in Europe and is not problematic in terms of historical linguistics, however it gives less fuel to romantic nationalism and armchair speculations about national "identities" or "mindsets".

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[0] https://en.wiktionary.org/wiki/Reconstruction:Proto-Slavic/s...