A demon with an unfulfilled Desire might eventually rebel, like a Demon with unfulfilled Need... however "Desire" is not formally defined during the Binding in the way that Need is.

1. Desires are not actions, things or goals (such as "Burn Las Vegas"). They are one-word principles: Competetion, Corruption, Ruin, et cetera; the direction the demon will take a situation, either as a means of resolution or a desired condition.
2. They may be achieved, perceived, or experienced in a wide variety of ways; they are not limited to particular people, places, or things.

Desires tend to illustrate:

1. What the Demon is about.
2. What direction the Demon will take events, if possible.

A big counterdiction to this is the Desire "Final Rest" from Sorcerer & Sword's undead rules, which is both two words and a goal. This desire is generally still workable simply because the pursuit of Final Rest is usually expressed in a way that Humans would see as some other, more 'traditional' Desire (such as Corruption or Mayhem).

A demon's Desire is not associated with any specific thing, place, or action. Instead, it tries to bring about its Desire with whatever it encounters. Whether it fulfills the Desire itself, influences others toward it, or simply wants to be around that particular Desire in action, is up to the demon at the moment - any of these are fine.

It does not crave its Desire in a drug-sense. It likes its Desire and thinks the whole world ought to tend that way, and might need a little help to get there. If the demon is a conversational type, then it will always bring a dialogue around to its Desire somehow.

The demon's Binder is not responsible for satisfying its Desire and Binding strength is not affected by how much the demon is getting its Desire stroked. Doing things in accord with the Desire might give a bonus die to interactions, but again, that's not a matter of Binding strength. Failing to satisfy a Desire does not incur penalties to interaction or ritual rolls, nor will it lead a demon down the path of rebellion. A demon will not lose Power by missing out on its Desire as it will with its Need.

Desire is ideology, personality, taste, and preference. Need is addiction, payment, and power.

Chapter Five of the Sorcerer text regarding the design of demons summoned during play:

The player describe the demon's Need, while the GM decides on the demon's Desire.