Tesla Loses World’s Most Popular EV Maker Title to China’s BYD

China’s BYD Co. bills itself as the biggest car brand you’ve never heard of. It might need a different tagline soon.

The automaker is poised to surpass Tesla Inc. as the new worldwide leader in fully electric vehicle sales. When it does — likely in the current quarter — it will be both a symbolic turning point for the EV market and further confirmation of China’s growing clout in the global automotive industry.

In a sector still dominated by more familiar names like Toyota Motor Corp., Volkswagen AG and General Motors Co., Chinese manufacturers including BYD and ...