I am a technical guy and had one concept. I have developed the concept into the web-application. I have secured domain name as well. Today, I came to know that the twitter name(same as my domain name) is already taken by an individual and he has been twitting since a long. I have not approached him for the twitter name yet. Can you please tell me how much important is twitter account with same name? Shall I approach that individual for the twitter account? or shall I create some other twitter account for my website?
Personally I don't find Twitter name that important. You can create a new twitter-name expressing your domain like NAMEdotCOM. If someone will search, he will find you anyway in twitter if you have the name of the domain somewhere.
Twitter names have been a problem (too many registered, not all being used) and there is little chance of getting that name you want if it is registered by someone else, especially if the guy is active and has some friends and followers.
There are some cases when Twitter names are sold (State of Israel bought @israel: http://www.ynetnews.com/articles/0,7340,L-3953977,00.html) but I would not recommend it in your case.
Even if you approach this individual, chances are you will not get their twitter username. Twitter is a social platform for conversation so for someone to give away their username is essentially giving away all their followers, and any credibility they have built.
That being said, who cares! Be creative. It's just a username. Having a unique and creative username may actually help you if it is creative enough to be memorable. You can always put your company name as your Twitter name (though I wouldn't recommend this) and also your company URL on your Twitter profile so everyone will know what your company domain address is.
Business will throw you curveballs all the time. If having your ideal username already being taken on Twitter is a big problem then smile because it's not really a big deal at all.