Google’s self-driving car project on Tuesday got an official name, Waymo LLC, and became a stand-alone business unit within the Alphabet Inc. empire, signaling that the effort will soon be expected to generate revenue.

The Mountain View, Calif., tech giant showed new willingness to work with partners to put its autonomous-driving technology in typical vehicles, indicating it isn’t totally wedded to developing futuristic cars without steering wheels and brake pedals.

“We...