Bret Taylor has been involved with some of the tech industry’s most notable innovations—from Google Maps to Facebook ’s “like” button—and founded companies that sold for hundreds of millions of dollars.

But until recently, the 41-year-old Oakland, Calif., native was largely unknown outside Silicon Valley. Then, within a couple of days at the end of last month, Mr. Taylor was named to help run two of tech’s most prominent companies, as board chairman of Twitter Inc. and co-chief executive of Salesforce.com Inc.