If you’re a traditional (offline) company you can create a domain name that doesn’t identically match your company name. For example, if you are “Widgets R Us” you could be WidgetsRUSonline.com or GetWidgets.com, and so on. Your offline brand and online presence don’t need to match 100%, although it’s desirable if they do.
Where everything breaks down is if you’re a pure Internet company. Then your domain is your brand. And there are virtually no domains left. Almost every word or word combination that isn’t pure gibberish has been registered. That’s why you see all these goofy and distorted new company names (unless they’ve bought the domain from someone else). It’s a backward way of doing branding.
Ordinarily one would sit in a room, come up with a brand and then establish a web presence reflective of that brand. But people nowadays have to back into a brand based on what domains are available (or pay the squatters’ extortion fees). Check out Go2Web20.net (itself an example). This a fascinating site that catalogs the Web 2.0 phenomenon in all its awkward-brand glory.
Only a fraction of these businesses will survive; so this will probably be the “Web2.0 graveyard” 18 months from now.