WASHINGTON—When news of an enormous Facebook breach broke last month, Chris Wellens couldn’t help feeling a little smug. After all, nearly all the information the technology executive had given the social media giant was false.

Consumers, wary of how their information is being used, lie about everything from names to birth dates to professions when companies ask for personal details online. Some are worried about identity theft, some just want to protect their privacy and some hope to fool advertisers by intentionally mucking...