Amazon.com Inc. has filed for a series of trademarks that suggest the company is planning to roll out more clothing brands, part of its bid to become a bigger fashion destination.

Over the past few weeks, the e-commerce giant has filed U.S. trademark applications for eight apparel lines, including ones aimed at outerwear and children’s gear. The company, which has built up its private-label clothing and accessories business over the past few years, already has dozens of brands in place in all kinds of categories, including shoes.

Amazon’s largest competitors, Walmart Inc. and Target Corp.,…