Generally, you can use your city in your business name. Of course, for every rule, there is an exception (sometimes, more than one). You cannot imply that your business is somehow a government agency, part of law enforcement or a financial institution. State laws vary in terms of the words you can or cannot include in your business name without the appropriate charter, so that’s one set of laws you’ll need to check.

Also, as a ballet studio, if you are offering classes (and not just room rental), you will need to check with your state’s Department of Education to determine whether you need special licensing or not. (If you are not providing certification or a guarantee of educational achievement, like a university, you may be exempt). There may be special wording in your business certificate or a special procedure for business registration that you’ll have to go through to qualify for the exemption.

Finally, you’ll want to be sure that the name of the studio isn’t already taken in your state by another company -- whether for-profit or not-for-profit. And which will you choose? Depending on the mission for your business, you could qualify as a B Corporation (if available in your state). All the more reason to work with an attorney who can check the regs and guide you through the questions you’ll want to ask, so that you get started on the right foot (pun intended).