You will need to check with your local, state and federal authorities on whether the business name has already been taken for most countries you can either do this online or at through a government agency. The second step is to check out your online competition, through domain and Internet searches to ensure that you will not clash with an already established business.
Make sure you chose a name you can live with and that will still be relevant with any growth or expansion of your business think long term to ensure you dont have to go through any losses due to re-branding later on.