In many European languages the words for bear have their origins in taboo avoidance. It is thought that people who spoke Proto-Indo-European (PIE) believed that if you called a bear by its true name, it would hear you and may harm you. So instead they used different names when referring to bears [source].
The words for bear in Germanic languages can be traced back to the PIE *bʰer- (brown), via the Proto-Germanic berô (bear).
Examples include bear (English / West Frisian), beer (Dutch / Afrikaans), Bär (German), Bier (Luxembourgish), björn (Icelandic / Swedish), and bjørn (Norwegian / Danish / Faroese) [source].
In Slavic languages the words for bear can all be traced back to the Proto-Slavic word medvědь, from *medu-ēdis, from medъ (honey) & *(j)ěsti (to eat), so could be translated as “honey eater”.
Examples are медведь (Russian), médved (Slovenian), medvěd (Czech), niedźwiedź (Polish). The Hungarian word for bear, medve, possibly comes from the same root [source].
In Baltic languages the words for bear from the Proto-Baltic *talk-, *tlāk-, from Proto-Indo-European *tel-k-, *tl-ek- (to push, to hit, to kick, to trample), and could be translated as “trampler”, “stomper”, “pounder”, [source]. In Latvian the word is lācis, and in Lithuanian it’s lokys.
The PIE word for bear was *h₂ŕ̥tḱos, which is possibly related to destroying or destruction – another taboo avoidance? This is the root of *artos in Proto-Celtic, άρκτος (árktos) in Greek, ursus in Latin and ari in Albanian, and related words in modern Celtic and Romance languages [source].