Is one allowed to use a business name that is similar to a name protected by a trademark if the services they offer are different?

Trademarks apply to classes of goods/services, not for everything.  The touchstone is generally whether a consumer will be confused into thinking that your product or service is being offered by the trademark owner.  Thus, you couldn't operate a hamburger restaurant named "McDonalds", but you could operate an autobody shop by that name.  In your particular example, it seems like a close question to me, and you may want to consult a North Carolina attorney who deals with intellectual property issues.  He/she would be able to get deeper into the facts and give you a better idea of your status.