Do you mean is having a domain important or do you mean is the actual domain name you choose important?
We started out without an official domain name years ago and everything was done over the phone/in person, but that was all local clients. If you plan to offer to anyone other than local, there wouldn't be any decent way to do it without a domain. Besides, with the cost of a domain being so low, there is no reason to not have one no matter whether you are catering to local/International customers.
As for the actual domain name, as long as it is easy(ish) to remember and people can return to your site easily, the actual name shouldn't really matter that much. A good easy to remember domain name that is catchy will work wonders for repeat visitors though.