When I think of the term Netflix, I think of watching flicks on the Internet. I'm sure a lot of people don't look at it that way, but the term Netflix makes a lot of sense when referring to a streaming service (as opposed to a service that rents out physical media).
I know a lot of non-savvy people probably can't make that connection, but I think the company will make it clear that Netflix is no longer the place for DVDs.