The third-tone
蒙 (often capitalised in pinyin since it's a proper-noun reading) is locked to the Mongol world:
蒙古 (Mongolia / Mongol),
内蒙古 (Inner Mongolia, autonomous region of the PRC),
外蒙古 (Outer Mongolia, the modern state),
蒙古族 (the Mongol ethnic group),
蒙古人,
蒙古包 (yurt, the iconic round felt tent). One handy commercial example: dairy giant
蒙牛 takes its name from the Inner Mongolian grasslands its milk comes from. Taiwan often reads even these as méng — mainland pinyin standardises on Měng.