You might find it interesting that the Kabbalists think our DNA is our name in a similar sense that they say the Scriptures are another name for God. Perhaps the language of the DNA (or such) will be used to rewrite our resurrection bodies with better stuff than the atoms we are made of now? As you said, nothing is beyond Gods ability.
It appears to me that the bodies which we are intended to have and will have in the resurrection are quite different from the ones we currently possess. After the resurrection, Jesus appeared in the midst of closed rooms, sometimes He concealed His identity, yet He ate and offered His body for physical examination by doubting Thomas. There was physical substance or not as He wished.
I conclude that our resurrection bodies will not be constrained to what we now call the physical laws - i.e. the limitations of the physical or material realm. Rather, we will be able to enter and leave as we wish, like the angels who appeared to Abraham, Lot, Daniel, Mary, etc.
Also, when Moses and Elijah appeared with Jesus, the disciples knew who they were. Abraham recognized the Lord when He appeared to him. And yet, Jesus sometimes concealed Himself and we are warned that some of the strangers we meet may actually be angels.
Seems to me that our resurrection bodies will be incorruptible, immortal, angelic. Instinctively, I believe those bodies will be whole and we will appear to others in eternity as they knew us, or in the alternative they will know us even if they had never meet us in mortal life at that age, in wholeness, etc.
Here are some Scriptures for Lurkers who may be interested in the subject:
Be not forgetful to entertain strangers: for thereby some have entertained angels unawares. Hebrews 13:2
And the LORD appeared unto him in the plains of Mamre: and he sat in the tent door in the heat of the day; And he lift up his eyes and looked, and, lo, three men stood by him: and when he saw [them], he ran to meet them from the tent door, and bowed himself toward the ground, Genesis 18:1-2
And there came two angels to Sodom at even; and Lot sat in the gate of Sodom: and Lot seeing [them] rose up to meet them; and he bowed himself with his face toward the ground; And he said, Behold now, my lords, turn in, I pray you, into your servant's house, and tarry all night, and wash your feet, and ye shall rise up early, and go on your ways. And they said, Nay; but we will abide in the street all night. Genesis 19:1-2
And there appeared unto them Elias with Moses: and they were talking with Jesus. Mark 9:4
Now when [Jesus] was risen early the first [day] of the week, he appeared first to Mary Magdalene, out of whom he had cast seven devils. Mark 16:9
After that he appeared in another form unto two of them, as they walked, and went into the country. Mark 16:12
And as they went to tell his disciples, behold, Jesus met them, saying, All hail. And they came and held him by the feet, and worshipped him. Matthew 28:9
And it came to pass, as they were much perplexed thereabout, behold, two men stood by them in shining garments: - Luke 24:4
And, behold, two of them went that same day to a village called Emmaus, which was from Jerusalem [about] threescore furlongs. And they talked together of all these things which had happened. And it came to pass, that, while they communed [together] and reasoned, Jesus himself drew near, and went with them. But their eyes were holden that they should not know him. And he said unto them, What manner of communications [are] these that ye have one to another, as ye walk, and are sad? - Luke 24:13-17
And it came to pass, as he sat at meat with them, he took bread, and blessed [it], and brake, and gave to them. And their eyes were opened, and they knew him; and he vanished out of their sight. Luke 24:30-31
And as they thus spake, Jesus himself stood in the midst of them, and saith unto them, Peace [be] unto you. But they were terrified and affrighted, and supposed that they had seen a spirit. And he said unto them, Why are ye troubled? and why do thoughts arise in your hearts? Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have. - Luke 24:36
But Mary stood without at the sepulchre weeping: and as she wept, she stooped down, [and looked] into the sepulchre, And seeth two angels in white sitting, the one at the head, and the other at the feet, where the body of Jesus had lain. John 20:11-12
And when she had thus said, she turned herself back, and saw Jesus standing, and knew not that it was Jesus. John 20:14
Then the same day at evening, being the first [day] of the week, when the doors were shut where the disciples were assembled for fear of the Jews, came Jesus and stood in the midst, and saith unto them, Peace [be] unto you. John 20:19
And after eight days again his disciples were within, and Thomas with them: [then] came Jesus, the doors being shut, and stood in the midst, and said, Peace [be] unto you. John 20:26
After these things Jesus shewed himself again to the disciples at the sea of Tiberias; and on this wise shewed he [himself]. John 21:1
Jesus saith unto them, Come [and] dine. And none of the disciples durst ask him, Who art thou? knowing that it was the Lord. Jesus then cometh, and taketh bread, and giveth them, and fish likewise. - John 21:12-13
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. So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory. O death, where [is] thy sting? O grave, where [is] thy victory? I Cor 15:52-55
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. Rev 21:4