There are a couple of important things to consider.  Even though you'll be providing the service for kids 5 to 14, it's their parents who will be making the decision to send them to class, so you won't actually be targeting different demographics.  Plus, as a new business owner, it's vital to focus on your best prospects and make them the target of your campaign.  Later, you can branch out to additional groups.

Yes, it is important to start with the right name.  The best names let people know what the business does or is about.  And, of course, it's terrific if the name you come up with also works well as a domain name for a corresponding website.  Look at some of the best company and URL names out there, such as Toys "R" Us, Books a Million, or even the domain name of a small URL called Perfectpuppy.com.  Stay away from nondescript names such as Jones & Co.  Always make it easy for your best prospects to find you in an online search and for passersby who see your company signage to understand what you offer.