Before you get started on logos/letterhead/illustrations/etc, why not check and confirm that your new name is not in use already. A great tool to help you determine the validity of your choice is UD Namecheck. This tools checks, with a single search interface:
- Domain names
- Social Media usernames
- Brand names (trademarked)
It's not an exhaustive list, but it is a good start and can serve your purposes pretty adequately. Check it out!