As stated in my previous response, the characters would remember any name that they regularly go by. This means that if they do not go by that name aside from in their past or in very mild interactions with people, then they will not remember that name.

I am not canon familiar with KH, but does Saix regularly go by "Isa" at the point in canon that he's taken from? Because if not, he would not remember that name.

I hope that clears things up!