No... for some reason it stays as the first one that I evolved it into. For instance: I evolved it into Quakeon then de-evolved it then evolved it into Glaceon, but its name stayed as Quakeon.
I am playing Aster Violet and I got to Sunny Town. I got the Eevee and the Synthetic stones. I decided to evolve it then de-evolve it but it kept the name of the Eeveelution that I evolved it into. Its not game breaking but it is annoying. Am I doing something wrong?