First of all, congrats on thinking of your new business name! It took me 4.5 months to think of my business name and make sure it wasn't already trademarked. If you're not sure it will be acceptable - try asking people you know. Find out if they think it works for your business and industry.
Once I was clear on what I wanted my business to be, then the name work started. Mine was about the same, had to make sure all the digital and social media properties were available plus the name wasn't trademarked, etc.