I have a licensed business in one state. My biz name is not trademarked. Can I sue a similar business in another state with same name for infringement

What you mean is that your business name is not registered as a trademark; that's important because a trademark is something you have, not something you do. If you have rights in your business name as an unregistered trademark -- which is possible -- you may be able to assert those rights in a lawsuit against an infringer. In order for you to prevail, you will need to show that that an appreciable number of ordinary consumers of the defendant's products are likely to be misled into believing that his products are made, authorized or sponsored by you. Your mark will also need to meet certain minimum standards of distinctiveness. If you want to discuss this matter on a professional basis, please call my office at (203) 399-1320.