Is anything incumbent upon him if he prayed Dhuhr, then during the prayer he thought it was Asr, and he realized that after the prayer?

The intention (niyyah) is a condition for the validity of prayer, and its ruling must be maintained, not just uttered. If a worshipper does anything that contradicts their intention, their prayer becomes void. If a worshipper intended to pray Dhuhr and then during the prayer, thought it was another prayer:

1. If they changed something in their prayer based on this thought, it has been said that their prayer is invalid and must be repeated. However, it has also been said that it is valid absolutely, which is the more apparent view according to the Shafi'is and Hanafis. 2. However, if they did not change anything that contradicted their initial intention, their prayer is valid.

The more apparent of the two opinions in this matter is that their prayer is valid, Allah willing.