I think an icon means something has become iconic to a group of people. A mere representation becomes iconic when that which it represents resonates with an audience. If there was a colony of moon people who had dogs with five additional arms, representations of these dogs could be an icon for the enormous love of moon people for their pets, if enormous love for their pets was common among moon people. But on earth a picture of a dog with five hands would not be an icon for anything because that does not embody a shared value. Icon is representation in a realized (as opposed to hypothetical) context.
*I guess to address the prompt more on topic, about who, anyone can create an icon because an icon can be created by anybody. It also seems things become icons accidentally because it's hard to know what an object will mean to how many people. One might try to make an icon and fail, or a thing might become an icon inadvertently.
Icons are defined by a mass social awareness of them and are therefor not created but shared. Icons are art which, by a participatory social system, have been made iconic.