We are individually named by another or others, most often by our parents, before we get the opportunity to name ourselves. To go by a self-authored name, in a one-name situation, is to go without a name that one was named by a person or persons other than oneself; so, an anonym could be regarded as a name of one sense that is other than and hence without a name of another sense. Or that's my current defense of a word I've taken a liking to.