This person would be called a ??? person.
There isn't one Objectivist
code for this. Ayn Rand's
comments in the preface to The Virtue of Selfishness
notwithstanding, some people with a good grasp of Objectivism prefer to use "selfish" in a pejorative sense. I am not one of them, however, and I agree with Ayn Rand that the equation of self-interest with evil is a cultural artifact that we must not keep reaffirming. What follows reflects my own usage.
"Selfish" means "concerned chiefly or only with oneself" according to my American Heritage Dictionary, 3rd edition. Now Objectivism holds that one should be selfish in the meaning of "concerned primarily with one's self." That means taking oneself as one's highest value and one's own concerns as paramount, but not ignoring the value of others. See our FAQ for more on selfishness.
But the Objectivist conception of selfish leaves a remainder, which is your "???"
I usually call people who are concerned only with themselves "solipsistic." (Solipsism is "the theory that the self is the only reality.") If I mean what people sometimes call a "greedy materialist" I might say the person is "short-sighted and grasping." Objectivists might also call some "selfish" behavior "hedonistic," "unprincipled," or, most damning in Objectivist circles, "subjective." If the right kind of selfishness is rational selfishness, presumably the wrong kind is irrational selfishness.
This would be a good question to ask on an Objectivist discussion list. You would probably receive a wide range of responses, and maybe some creative ideas.
I hope my answer is helpful. I don't have time to survey the full range of Objectivist writers, but if you want to pursue this further, see what writers like Ayn Rand, David Kelley, Roger Donway, Nathaniel Branden, Leonard Peikoff, and Tara Smith use.