Have you checked? The name you want may already be taken.
What is Cybersquatting? Back when the web was new, many large companies had not thought to secure the domain names to their own company. Cybersquatters had acquired the domains in the hopes of reaping a profit from these companies when they got around to building their corporate web sites.
Is something similar happening on Twitter?
I think many e-savvy companies have already staked out some of their territory. That is their own names. However, I have noticed others have secured a number of user names with pretty good strategic value as well.
askthedoctor
medicalhelp
kitchendesigner
You get the idea.
Do you have a plan on how your company or brand is going to use Twitter? If not perhaps you should start to craft one now. Securing the appropriate user name may be more difficult than you think.