Using a pen name or a pseudonym in writing letters to the editor or essays or a book might seem like lying.
Is it Halachically permissible?
While this may be considered anecdotal evidence, there were quite a few famous works that were originally published anonymously (although it often eventually became known, and sometimes became the new title of the author), which leads to the belief that it is indeed permitted.
See below for a partial list:
From the comments to the question:
As was mentioned in the comments to this answer, the first examples given may be 'anonymous' names, but not necessarily a 'pseudonym' name. However, it seems like the names in the list of works from the comments would be classified as 'pseudonyms', which leads one to the conclusion that indeed, it is permitted to write as a pseudonym.
We need to distinguish between lying and changing things (seems like a tautology, but it isn't).
Lying, which is denying or negating the truth is bad, agreed (see Gemmorah Shvuos 31, Chinuch 74, Sma"G 107).
Changing things for noble purposes is permitted, based on Gemmorah in B"M 23b:
"בהני תלת מילי עבידי רבנן דמשנו במלייהו " (those are the three things the Sages change their words)
The examples are numerous, see also Shu"A Cho"M 262, 21, Mishna Berura 85,8 and many many more on different ways of changing one's speach.
Choosing a pseudonym that is an explicit lie, especially if someone can be hurt is prohibited (for example signing your brother's or your friend's name or some Rabbi's without his permission).
Using a pseudonym that is not a lie, but an arbitrary, usually a streamlined or shortened form of a name, as one is Halachicly allowed to alter his name, it is permitted.
And especially if there are some benefits for the writer (or less shame or disgrace)