An Etymological Dictionary of the German Language/Annotated/Bär
Bär (1.), masculine, ‘(paving) beetle,’ from Middle High German bęrn, ‘to strike, beat,’ whence also Middle High German bęr, feminine, ‘blow, stroke.’ Old High German bęrjan, Gothic *barjan, agrees by the permutation of consonants with Latin ferio, ‘I strike,’ as well as Old Bulgarian borją, ‘I fight’ (Old Icelandic berjask, ‘to fight’); it is based on the root bher, ‘to strike.’
Bär (2.), masculine, ‘bear.’ The Latin name of the animal (ursus) descends from the pre-Aryan period, just as Greek ἄρκτος and Indian ṛkša-s (ursus for *urcsus). It is remarkable that the Teutons have abandoned this old Aryan term for ‘bear’ (ṛksós, Teutonic orhsa-s), since they have retained other names of animals. In Middle High German we have bër, Old High German bëro, Anglo-Saxon bëra, English bear, björn, ‘bear’ (Gothic *baíra). The Teutonic beron- is a substantive form based upon an Aryan adjective bhero-, equivalent to Lithuanian bėras, ‘brown’ (Latin furvus?), from the root of which, bher and Modern High German Biber, braun, may also be derived; in using the adjective as a substantive the Aryan ṛksos is understood. Note that Braun is the name of the bear in the Old German animal fables.
Bär (3.), masculine, ‘brood-boar,’ from the equivalent Middle High German and Old High German bêr, masculine, which, with Old Saxon bêr-swîn, Anglo-Saxon bâr, English boar, points to Gothic *baira-.