SHANGHAI—Honor, the Chinese smartphone brand and Huawei Technologies Co. Ltd. spin-off, saw shipments soar in the latest quarter to become the country’s third-ranked brand, said research firm Counterpoint Research, which tracks hardware. The brand’s swift rise comes after Huawei saw sales tank following sanctions imposed by the United States that prevented it from sourcing chips. Honor sold 9 percent more phones in the quarter ending in late September than in the corresponding period a year before, said Counterpoint, to grab a 15 percent share of the market in China. It now ranks after Vivo and Oppo, that have 23 percent and 20 percent of the market, respectively. Honor originated as a sub-brand of Huawei that specialized in low-end and mid-range devices. This year, Huawei said it had sold the division to a consortium of buyers including the government of the southern boomtown of Shenzhen. The company has ramped up advertising …