If the company is registered in different cities, it is impossible to have the same name, because in Zhengzhou, you can only be approved as "Zhengzhou Jiajia Food Co., Ltd." when approved by the Industrial and Commercial Bureau, while in Shijiazhuang, you can only be approved as "Shijiazhuang Jiajia Food Co., Ltd.". The enterprise name management method stipulates that the enterprise name approved by the same industrial and commercial authority cannot be the same or similar in the same trade name, so the enterprise name approved by the same industrial and commercial bureau will not appear in different cities. It can be said that you can go to another city without prohibition. However, if Jia Jia is a registered trademark or a well-known trademark, you can't use "Jia Jia". Article 58 of the Trademark Law stipulates that if another person uses a registered trademark or an unregistered well-known trademark in the name of an enterprise to mislead the public and constitute unfair competition, it shall be dealt with in accordance with the Anti-Unfair Competition Law.