This is a common dilemma- how do you maintain a consistent brand image across multiple websites?
First, this is an issue even for even larger companies, even before the age of the internet. For example, companies like Neutrogena would sell things like Lipstick, Shampoo, Deodorant, you name it. Their solution seems to be to simply put "Lucky Lipstick, by Neutrogena".
The most common internet retailer in this situation is probably hayneedle.com (revenues $300m +) who run 200+ niche websites. As you can see, the name of the site almost seems to be an afterthought with them. Everything is branded as Hayneelde first and the name of the website secondary.
So with that being said, a couple of things to keep in mind IMO. First, your corporate name doesn't necessarily have to reflect your brand. KFC is part of Yum Foods. It can simply be your legal name. But for smaller companies, it's probably easiest if the Corporate name is your brand name as well. Just don't make that legal name limiting...don't call yourself "Joe's Bicycle Wheels Inc." if you think you might sell car wheels down the line. Make yourself something more inclusive like "Joe's Wheels Inc." or just "Joe's Parts Inc".
Second, and probably most importantly, a brand image is more important than a brand name. Your websites should all have a consist look and feel. Your policies should be consistent (don't have free shipping on one site and $9.99 shipping on the next). And of course, the overall customer experience should be the same.