In a business purchase agreement there should be a non-compete clause protecting you from this exact circumstance. If an attorney prepared the agreements with you, consult with him to find out if the contract allows you to get an injunction.
In buying a business, obtaining a covenant not to compete is essential to protecting what you buy.
The issue comes down to whether you obtained a covenant not to compete or not. The fact that you did not mention one suggests that you did not get one as part of the deal. Even if you had one it would be subject to "reasonableness" and this may or may not apply to a neighboring city.
Another thought is what exactly you bought and this would require a review of your contract to see whether you paid for what they are not using. There may be a claim for a business tort (wrong) if they were acting with malice or evil intent and you can prove it.
Lastly, you may wish to consult with a local intellectual property or trademark attorney to review the similarities and advise you on whether there was a misappropriation of an advertising ideas or style of doing business or a copyright, title or slogan.
You may have recourse here or not, but the best thing to do is to schedule a consultation with a business attorney as soon as possible. You do not want this to go on for too long a period so that you avoid a claim that you consented.
We would need a lot more details in order to give a good answer. You need to consult with a lawyer who is experienced in handling business purchase and sale transactions. They will need to review your purchase and sale agreement. A well written purchase and sale agreement should address the issue of who owns the trade name. If it does not, you should consult with a legal malpractice attorney as to whether the attorney who prepared or negotiated the agreement for you has some liability in this situation. If the document was prepared by someone who was not an attorney (real estate agent, business broker, etc.), they have the same liability for legal malpractice as an attorney. An experienced business attorney should be able to help you determine what your rights are and whether you have possible recourse against anyone. Good luck.