Reverse narcissism is an infrequently used term referring to covert narcissism. Covert narcissism is a less obvious form of narcissism than what is usually referred to when describing the disorder. Often the person with covert narcissism seems shy and reserved, but this hides grandiose fantasies and thoughts, a sense of entitlement, and an overall sentiment of being better than others. They are often referred to as vulnerable narcissists to suggest they experience low self-esteem and distress because others don't treat them the way they know they deserve to be treated. They tend to not be loud, outwardly vain, obvious braggarts. Yet they are still every bit as arrogant and argumentative as people with the more outgoing brand of overt or grandiose type of narcissism.
That being said, research shows that all narcissists display both covert (reverse, inverted) and overt (grandiose) characteristics. They may have a tendency to show more of one or the other, may switch between the two, or consciously employ one type in certain situations and the other in different situations. It has been suggested that overt and covert are simply different types of expression and not actual types of narcissism.
Please see https://healdove.com/mental-health/Differences-Bet... for a more complete discussion of covert and overt narcissism.