The new Waymo CEO, John Krafcik, sums up the name and the mission in his blog post on Medium:
Today, we're taking our next big step by becoming Waymo, a new Alphabet business. Waymo stands for a new way forward in mobility. We're a self-driving technology company with a mission to make it safe and easy for people and things to move around.
He then gives an idea of their future plans:
Our next step as Waymo will be to let people use our vehicles to do everyday things like run errands, commute to work, or get safely home after a night on the town.
The Waymo fleet of vehicles currently includes 24 Lexus SUVs, 34 of the small two-seater prototype 'bug' vehicles, and there is a collaboration with Fiat Chrysler Automobiles for 100 Pacifica Hybrid minivans. The first sightings of these Pacifica have already been made.
There are no details about where Waymo might deploy their vehicles as a pilot project, but of their existing test sites, Austin, Texas might be the most likely candidate as the climate and the traffic conditions are more favorable than the other locations where they have been operating in Mountain View, Phoenix, Arizona, and Kirkland, Washington.