Adopting a possessive company name such as Bob’s Vital Signs or Victoria’s Secret might be effective for some companies, but not for all.
A possessive name will connote a less formal, more friendly business – one delivering personal and responsive services. But it just doesn’t seem appropriate for a bank or a valve manufacturer or many other business types.
They certainly seem more appropriate for local service businesses. But therein lays the rub. You’ll find hundreds of businesses with possessive names in your local yellow pages. So to make your name unique, the second word, the object being possessed, should be unique. That will help you differentiate the business. (And it doesn’t hurt having the possessive be unique as well, even if it’s fictitious)
With this approach, even a world-wide business might be comfortable, even successful, with a possessive name. It certainly worked for Victoria’s Secret.
So look beyond a definition of your service/product category. If you’re a mechanic, think about something like Otto’s Motive.
Another variation: just use a one-word possessive without tacking on an object. But for this approach to work, the possessive must be really unique, as in the name I created for a local day spa, Molly Coddler’s.