People write for many different reasons. However there is, let’s be honest, a part of the process of being published which plays to the ego. Many find it nice to have a book published and see it sitting there on the shelf by your desk with your name on the cover. Similar feelings may accompany the publication of an article (and, yes, a column like this!).
Yet sometimes it may be right to avoid this. It is said that JK Rowling’s name was presented like that to make the gender to which the author belongs unclear (though we all know now of course). Other authors have changed their names to make them specifically appear to be one gender or another or to make them shorter or easier to pronounce. Or to avoid been mistaken for someone else with the same name; if my name was Frederick I would surely not have been published under my own name. Sometimes co-authored books have one name on the cover (for example, Nicci French). Twice I have had several books published within a single series and been asked by the publisher to adopt another name for one of them, just so that the series appeared to have contributions by a greater number of authors. In some ways I, perhaps like most writers, resist this and always prefer to have my own name on the cover.