Utiliarianism is so called because it is concerned with 'utility' Bentham makes this connection between utility and happiness.
By utility is meant that property in any object, whearby it tends to produce benefit, advantage, pleasure, good or happiness or to prevent the happiness of mischeif, pain, evil or unhappiness to he party whose interest is considered.
Thus, somethign has utility if it contributes to your happiness, which is the same as what is in your interest. And happiness is pleasure and the absense of pain. The claim that pleasure, ashappiness, is the only good is known as hedonism.
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