Was the blotting out of their names predetermined also?
"Like them, he who overcomes will be dressed in white. And I will never blot out his name from the Book of Life, but I will confess his name before My Father and His angels."
In the scripture above, Jesus is speaking to the church of Sardis and to all of those believers who would fall under the same rebuke of soiling their garments, which would be a reference to the indulging in the sinful nature and living in the world. Of those who have soiled their garments, if they repent they will also walk in pure white garments and Jesus will not blot out their names from the book of life. If they do not repent and remain soiled, then I believe that Jesus can and will blot out names.
Just to be clear about this matter, though I believe that it is by God's Sovereign election that people are saved and that before the world began, however, our salvation is still dependent upon our continuing in faith. As believers we can't just go back to living according to the sinful nature and still expect to inherit the kingdom of God. Faith is what connects us to God's grace. Like an electrical plug in a wall outlet, we must remain plugged in to God's grace. For we are saved by grace through faith. Regarding this, consider what James wrote:
"My brothers, if one of you should wander from the truth and someone should bring him back, consider this: Whoever turns a sinner from the error of his way will save his soul from death and cover over a multitude of sins.
My brothers = He is speaking to believers
wandering from the truth = one who was once in the truth, but has turned away from it
While in the wandered state = one is accumulating sin and is on their way to death
So, though God has chosen those whom He saved, they must continue in faith. Regarding whether or not names being blotted out as being predestined, I cannot answer. But I know that their calling was predetermined.