No.
Generally speaking, even the elders (in recent generations, it is difficult to name them if they are far away) should not be able to do it. It is to prevent collision with elders. For example, if A and A's father both have the word "A" in their names, if they are both called "Xiao A" or something like that.
Chinese people attach great importance to ethics and morality. That is to say, father and son are related, monarch and ministers are righteous, husband and wife are distinguished, elders and young are in order, and friends have trust. These five moral ethics are unchangeable and constant, so they are called "moral ethics". Only people of the same generation can have the same characters in their names.