Zhang Jiaxin, Zhang Jiacheng, Zhang Jiasheng, etc. are all OK.
I know a little about the Five Elements and Eight Characters, and I can help you analyze why you should name it like this.
A person was born at 22:37 on February 21, 2022 in the Gregorian calendar. The birth time corresponds to the lunar calendar: 21st Hai hour in the first month of 2022.
The eight characters correspond to: Renyin year, Renyin month, Yisi day, and Dinghai hour.
The five elements correspond to: water and wood, water and wood, wood and fire, fire and water.
There are 3 wood, 3 water, and 2 fire in the five elements, and there is a lack of gold and earth.
The child’s surname is Zhang, and his courtesy name is Daijia. There is only one character left. He has to choose between gold and earth. My suggestion is to choose gold.
In the name "Zhang Jiaxin", the five elements of Zhang belong to fire, the five elements of Jia belong to wood, and the five elements of Xin belong to gold.
The name still lacks earth in the five elements, so it is recommended to bring gold and earth in the nickname.