It will just be a brand name to them and they'll use the one that best suits their needs. If they don't like their transactions being public knowledge, I think they'll use DarkCoin, otherwise they'll use Bitcoin.
The media, the logo on the site "darkcoin accepted", all that implies for my mum, my collegues, my neighbour a much more evil coin than silent-coin/secret-coin/private-coin.
I think it's the only (but important) flaw of that coin.
I definitely think it could be better. PrivateCoin is a much more fitting. But I just don't think it will be too much of a problem. Not every association with dark is bad. With a better logo and professional branding, it wouldn't be a problem.
also, brands can shake off stigma. people still drink coca cola even though the company once used cocaine in the drink.