More self-named can be replaced with a variety of synonyms, depending on the context. For example, one could use the term self-proclaimed, which denotes someone who has claimed a title or status for themselves. Another option could be self-titled, which is commonly used in reference to albums or books where the artist or author has chosen to name the work after themselves. Alternatively, one could use the term egocentric or self-absorbed to describe someone who is overly focused on themselves and their own accomplishments. Ultimately, the choice of synonym will depend on the specific connotation desired and the traits or behaviors being described.