My question is : what was the philosophy behind 10th Imam’s choice for naming his daughter Ai’sha? many Sunnis ask why we don’t name our daughters Ai’sha? And they give 10th Imam (s) daughter for example. What should one answer?

It is one of the common names. It has nothing to do with Prophet’s wife. It is a culture only. Here in Gulf area, people do name Aisha.