Probably from resha' with a prepositional prefix; with wickedness; Birsha, a king of Gomorrah -- Birsha.
see HEBREW resha'
H1306. Birsha
בִּרְשַׁע proper name, masculine (√ & meaning unknown) king of Gomorrha Genesis 14:2.
בֵּר֫וֺתָה בֵּרֹתִי, בֵּרֹתַי, see below בארות, p. 92.
בשׂם (have a sweet odour, compare Aramaic בְּסִים, be sweet, pleasant, Pa`el to delight, בַּסִּימָא, sweet; Palmyrene בשימא (משחא) VogJAs 1883, Août. Sept. 153 1. 12, 155 1. 16, 18, 20 etc. spiced (oil), compare ReckendZMG 1888, 403; Assyrian bašâmu, Pa`el make fine, beautiful COTGloss).
בֶּ֫שֶׂם, [בָּשָׂם] see בּשֶֹׁם. below