I think the challenge for Netflix here will be to disassociate Netflix with DVD rentals. People will go to Netflix's website, and expect their DVDs to be there alongside their streaming movies.
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.
When I think of Qwikster, I do not think of anything related to DVD by mail. The only associations that come to mind are Friendster and Quixtar. It sounds cheesy and cheap and fly-by-night.