A few things to consider for selecting a company name and domain name.
The company name
Research what is usually being done in your area of activity or profession. From there, you start brainstorming on a company name taking into consideration numerous factors such as but not limited to: the way you will be conducting business (online strictly or will you operate a storefront or have an office etc.), whether or not your company will provide products/services locally, nationwide or even worldwide and ultimately how well you, as an individual, are already known in your market or targeted market.
Keep in mind that down the road, you can always establish a “dba” or “Doing Business As” name if your company name is not appropriate for branding or opening a store location.
The domain name (or Website URL)
First of all, you could have more than one domain name pointing to the same website. This is commonly done. Secondly, your domain name does not necessarily need to reflect your company name. Having a domain name that reflects the company name is crucial for brands such as Apple, Dell, Virgin etc. but this is not crucial for most small businesses.
What is much more important is to choose a domain name that will help with search engine indexations and which speaks for itself.
Lastly, when you have a list of a few possible domain names, check their availabilities on the Internet (i.e. NetworkSolutions.com). A .com (dot-com) name is more desirable than any other extensions.
Good luck in your new venture!



