A penname is a name that one writes under (actual pen optional). If you want to sound fancy and highfalutin', you can say it in French: nom de plume. It is similar to a username in that it is not normally the writer's actual name, but instead an assumed name. On various fanfiction archives, one's penname is the same as their username.
We don't generally like to judge a book by its cover, but there has been an observed correlation between the quality of the penname and the quality of the writer's work. For instance, "Leggy_rox_my_sox23" is probably not going to have as good a story as someone with an original penname, or at least no unnecessary numbers, xs, dashes, and underscores. This correlation may be related to the writer's willingness to put more than five minutes of thought into how they present themselves. On the other hand, it may have more to do with the age of the writer when they made the penname, so it may be wise to give them the benefit of the doubt.