Well, not sure it is that easy. I haven’t seen a Mycena with that sort of shaggy margin. That might not mean anything…
I have seen many a Psathyrella with a brown cap and a white shaggy margin, that is small and terrestrial, and with a white stipe. Here you say it is a Mycena, not a Psathyrella.
So, to tell the difference it would be good to see what the fertile surface looks like, and maybe get a hint of spore color off that. Even then, getting a Psathyrella id just off one photo of the top of the cap, not sure people can do that.
Maybe someone knows a Mycena that looks like this one?