There is no unified statement on whether to change your mind when making an engagement. Because of different regional customs, traditional customs are also different.
In southern regions such as Fujian, Jiangsu, Zhejiang, and Shanghai, the traditional wedding ceremony of engagement is highly valued, while marriage is seen as just a ceremony. Therefore, parents of both parties will give red envelopes to the newlyweds during the engagement, and the newlyweds usually change their names to "dad, mom" after the engagement.
Compared to the southern regions, the northern regions place more emphasis on wedding ceremonies. Parents of both parties usually drink the newlyweds' modified tea on the day of the wedding ceremony and give them modified red envelopes; So in the customs of the north, it is usually changed to "dad, mom" after the wedding ceremony.
In fact, there are not so strict regulations on when to change one's mouth. As long as both parties reach a consensus, one can change their mouth at any time.