It really depends on your vision for the company and its product.
If you're building a singular brand/idea the single name works for product and company. i.e. FaceBook, LinkedIn, Twitter. It's generally cheaper to build a single brand name.
If you're building a company with a vision broader than a single product, keep the names distinct. i.e. Apple, Microsoft, Ford. Multiple products can get positive halo benefits from the company brand if you establish both carefully. i.e. Anything new from Apple has instant cred for many people.
Sometimes a company starts with the singular focus and moves towards a broader one. Google was initially the product and the company. Now you have gMail, YouTube, Google Voice, Google Analytics, Google Webmaster Tools, Google Drive, Google Play, etc. You'll notice that other than gMail and the purchase of the YouTube brand, it's been tough for Google to brand a product name that's distinctive. They end up attaching 'Google' to everything. Microsoft then follows with Microsoft Analytics and there's no 'brand' established by either.
Unless it is a 'build and sell' play, I think it's generally safer and creates more discipline to separate the product name from the company name and build both brands over time. This keeps your options open and forces you to establish clear visions for the company and the product(s).