There are many tomes written on brand management so I will not dwell too long on this topic here.

In summary, your brand is the personality or thoughts that come to the mind of your customers when your company name is announced.  The events that surround your company, the interactions with all of your external touch-points, and your promotional investments, will build "equity" in your brand image or destroy it.

In an ideal world, your brand message evolved on its own from your core competencies or founder and the brand name literally means what you aspire to be and the experience you deliver.  This ideal zeal is personified by every one of your employees and sales people.  It would never be any other way, right?

In a non-ideal world, multiple names, conflicting messages, and inconsistency can lead to brand confusion and be literally be disavowed by your employees. When I first came to National, the company allowed itself to be described in no less than 7 ways (National Semiconductor, NatSemi, NS, NSM, NSC, National Semi, and National).  The company also had a series of tag lines that added to this dissonance.  It took time but we were able to reel these in to one name, "National".  Even when the company was acquired, we still had minor issues with some regions of the world continuing with a local preference.  These nicknames die hard once they get established.  The lesson learned is to be maniacal about how you refer to your company and enforce it.

If your strategy is captured well, and your desired brand is real and credible (authentic/valid), you can devise programs to promote your brand and get your entire company to project this message.  This brand will resonate and build equity if your delivery is consistent.  This brand "voice" book or guide has to be enforced permanently.

Let's face it; none of us has infinite marketing dollars and you want to get the most out of what you have so investing in one name over an extended period of time is ideal for brand equity.