"But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up. Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness, Looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat? Nevertheless we, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness." (2 Peter 3:10-13)
"And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away. And he that sat upon the throne said, Behold, I make all things new. And he said unto me, Write: for these words are true and faithful." (Revelation 21:4-5)
Anchored or stored: "and the elements shall melt with fervent heat", " . . . all these things shall be dissolved . . . " (2 Peter 3:11a) , " . . . for the former things are passed away. " (Revelation 21:4b)
The details of personality and how it is related to the immortal soul are obscure to say the least. However it is interesting to note what the Bible has to say about the end of the present world and the creation of a new world. There seems to be a wiping out of some aspects of what is "in" the brain ( like synaptic connections and the individual electro/chemistry that has something to do with personality ) when the brain with all the elements of the cosmos "shall melt with fervent heat".
Then there is this: "Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away. For we know in part, and we prophesy in part. But when that which is perfect is come, then that which is in part shall be done away. When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things. For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known. And now abideth faith, hope, charity, these three; but the greatest of these is charity. " (1 Corinthians 13:8-13)
Personality elements like "Tongues"(= language), they shall cease; "Knowledge" shall vanish away.
What is it that remains? Faith, hope, and love which is the greatest of the three. Those are the essential character of Christ (God is Love) that is imparted to us in salvation. The "Beloved Disciple", John, said this, "Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is." (1 John 3:2) When we "see" Jesus we will be transformed into His likeness. The Apostle Paul said "In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal must put on immortality." (1 Corinthians 15:52-53) Changed in the "twinkling of an eye", instantaneous change into the likeness of Jesus.
And it's instructive to recall that God said to Moses, "And he said, Thou canst not see my face: for there shall no man see me, and live. " (Exodus 33:20) To see the face of God destroys the flesh, but the redeemed shall see Jesus as He is and be instantly changed into the His likeness and put on the newness of life immortal. That is the blessed hope of Christians. And it is through the shed blood of the Lord Jesus Christ that we are redeemed, "But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin." (1 John 1:7)