It's hard to say for sure however, magazines get hundreds of submissions every week, which makes it impossible to give specific feedback to everybody. There is as much competition for short story submission as for published books i.e. only a handful of slots available for a hundred or more submissions, so the success rate is slim.
I don't know how much you've been submitting that story around but when I used to write short stories for every short story I got published I had at least a dozen rejections from other publications. I had stories I submitted around for over a year before it got accepted somewhere, etc... There are a few writers on here who have had short stories published and they pretty much all have the same experience.
I doubt that you were rejected because you owned up to using a pen name, more likely that it was good but maybe they had better that week, or another story fitted more closely with what they were looking for, or it didn't completely win over the editor, etc...
My advice is just keep submitting and if you still keep getting rejection then re-evaluate and edit some more before submitting to more publications.