Groupon Inc. may be the undisputed king of Internet coupons in the United States. But with its March launch in China, the Chicago firm has stepped into a cutthroat market with thousands of competitors — including a copycat that’s using its name. Rechristened in China as, evoking a saying to gather honored guests, Groupon is hoping to seize a foothold in a country that’s increasingly turning to the Web to trade goods and services.