One could certainly make the argument that Alphabet's (GOOG) - Get Report(GOOGL) - Get Report Waymo segment is leading the autonomous driving revolution.

How so? The company has been quietly testing its robo-taxi business in Phoenix for the better part of a year, easily beating its competition to the punch. The question is, will it continue to beat them?

There's a bevy of competitors coming into the robo-taxi business, with General Motors Co.  (GM) - Get Report , Ford Motor Co.  (F) - Get Report and Uber planning test fleets and markets. Nissan (NSANY) is planning a robo-taxi service in Japan as well. In short, there's going to be no shortage of autonomous driving transportation services to choose from.

Waymo isn't taking its foot off the pedal, though. It recently said it will add 62,000 vans from Chrysler to its fleet by the end of the year and is currently providing about 400 rides a day in Phoenix. Waymo has also inked a deal for 20,000 Jaguar I-PACE vehicles. No one else is anywhere close to that scale right now, although that can change in a hurry. That's why Waymo's focusing on expansion.

It's not clear where it's next stops in the U.S. will be, but we now know Waymo at least has its eyes on Europe. CEO John Krafcik said the company will need "a large number" of cars to expand across the pond.

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Waymo is now logging about 1 million miles in month in real-world test driving

To be fair, he said both continents need them, but the fact that he's talking about expanding overseas is something to take note of. Krafcik also said the company will likely launch under a different name in Europe, because the "Waymo" name is not well known.

That's sort of a surprising tactic.

While Krafcik didn't say it, his comments imply that Waymo is a well-known brand in the U.S., although I would question whether that's the case. In the investment community it may be, and perhaps the people in Phoenix know of Waymo. But ask a handful of folks on the street what Waymo is, or if they know the name of Google's self-driving car business, and I have my doubts many will.

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Krafcik has got Waymo farther than any other brand though. So if he feels that going with a different name is right for Europe, who am I to argue? The question will be, what automaker or automakers will the company use in the region? So far, Krafcik said he wants to keep those names confidential for now. If Waymo won't use its own name, it's likely the company will partner with a more well-known automaker in the region. 

The question then becomes, who will it partner with? As we already said, Waymo currently works with Fiat Chrysler (FCAU) - Get Report , as well as Jaguar, so there would be options there. But going with a company like Mercedes (part of Daimler (DDAIF) ) might be another option. It's unclear if Mercedes would want to partner with Waymo, though, or work on its own technology and services alone. It has the versatile fleet that might make it attractive for Waymo, though. 

There's a long road ahead for Waymo -- or whatever the company will call itself over there -- but it will be interesting to see when and in what form the company launches overseas. At one time, there were serious questions about how Google would profit from its autonomous driving efforts. But it's becoming clear just how it will do so and its industry-leading technology is helping pave the way. 

This article is commentary by an independent contributor. At the time of publication, the author had no positions in the stocks mentioned.