Making your product name a Brand Name means that your product has to stand for something. The first corollary to this rule is that your product can’t stand for everything.
Think about it. Brands are just as much about the customers that they don’t/won’t sell to as they are about the customers that they want to sell to. Just like people. How many Democrats out there are more or less just Non-Republicans. Has anyone seen the Apple commercial with the Mac and the PC personified.
Compare this to your company. Sure, you have your target market, your core demographic that your product is made for. Then, since you are on the shelf anyway, you might as well get as many customers as you can. Why not tweak the package or raise/lower the price.
This is a great way to kill your brand, or not build it at all.
Once you add this or that target market you lose your identity you no longer stand for the what you used to stand for.
My advice to build your brand is to take the 10-20% of your customers that are the biggest pain in the ass (classified by market demographics) and get rid of them, surgically. Stop offering the benefit that they buy for. These customers aren’t loyal anyway and they are killing your brand.
A picture is worth a thousand words. The Porsche minivan.