[MBCook]

I agree. My immediate thought was something more akin to 'motor pool'. Maybe a way to pre-buy a group of rides at the same time or to the same place, such as getting friends to/from a party, for a discount.

Or perhaps it could have been a service where Uber had their own fleet of 'special' drivers for 'premium' members to help with peak demand times. Of course, this sounds quite a bit like a traditional contracted car service.

UberShare seems more fitting to me. Having read what it is the name makes sense, but it didn't inform me going in.