Is There Evidence That Noah's Name Was a New Name?

Noah was supposed to relieve the hard labor caused by the curse on the ground, and thus he brought rest. Noah has at least a partly symbolic name like adam, which is a sign that we shouldn't press the detail literally as if he had to be called this during his lifetime. It may well be that this is one of those after the fact names that biblical authors sometimes give to earlier individuals - sometimes for symbolic reasons.