A DNA molecule is still a DNA molecule, even if its nucleotides are rearranged.
Well, yes and no. DNA is a junkbasket name for a roughly infinite family of polymers of nucleotides. Each individual DNA strand can be named as its own unique molecule, just as each protein can be named either by a trivial name like "hemoglobin" or a very specific name like "glycilphenylalanylserylglutamylalanylalanyl....................................lysine. With DNA you normally see letters - A, G, C, and T - because it takes less ink.
A car is still a car, but a Yugo and a Maserati don't share all their functions.
Edited by Coragyps, : typo