Using Your Business or Domain Name
I touched on this earlier and I will mention it again. You can use your domain or business name as your username and you can fill in that business or domain name in the Name text box on the Settings page for your account. However if you do, be sure to include your name in the 160-character "Bio" text box on the Settings page for your Twitter profile. It is all about branding and just like you will want to have an About Me page on your website, you should fill in the Bio section of your Twitter account using your actual name.
Important to Note
Your Twitter username has power and influence on SEO which translates to how close to the top of a search results list you will appear in a search engine. If you're using your domain or business name, consider using a valuable keyword as your Twitter name. Ranking is everything.
My nickname locally in the bottled water biz is Water Dude so I'm TheWaterDude@TheWaterDude1 for a lack of something better....I might change it if I can think of something else.
You're right about the 15 characters though...I wanted it to be my website but it is way too long for Twitter.
BTW if anyone wants to follow me I'll have 1 follower!
Thanks Steph!