Utilitarians believe that moral behavior is about securing the greatest good for the most people. But what would you call people who believe moral behavior is about securing the greatest good for the most "good" people, or maybe securing the greatest good for the "best" people? Perhaps they might even believe moral behavior is about securing good for "good" people and harm for "bad" people.
Suppose a bolder is rolling down a hill toward two people, who are frozen with fear or otherwise unable to move. One volunteers at a homeless shelter and the other is a convicted murderer. You can push the boulder to one side or the other, but only a little. You must choose to save the volunteer or the mass murderer. According to utilitarianism, there is no rule applying immediately that would cause you to choose one or the other. Perhaps you might suspect the murderer might strike again, but ignoring that possibility you would have to flip a coin to choose which potential victim to save.
Someone subscribing to this philosophy might decide the volunteer is a good person and the murderer is a bad person, and for that reason decide to save the volunteer instead of the murderer.
Some of these people might divert the boulder toward two "bad" people away from one "good" person or even start the boulder rolling themselves, being careful to aim it at the "bad" person and miss the "good" one.
EDIT: To clarify, I'm wondering if the above describes a particular school of thought with a name and not so much how many people subscribe to it.