If you are writing under an other name, I am assuming this is done as a way to stay anonymous, or otherwise not have such writing associated with your name. Which means the public is less likely to know it’s you. Which means there can certainly be a perception of plagiarism. And once the perception is there, the technicalities don’t really matter much do they? You’ll be thought of as a thief.
It seems to me like you could certainly have to deal with all the backlash of plagiarism if you start writing the same story under different names, even if it’s ethically you’re not doing anything wrong.