If any desire you have excites you, and you allow it to come to fruition in an effortless way, then that desire is not ego driven. Conversely, if you feel that you simply must have your desire at any cost and so you try, struggle, force and push, then your desire is ego driven.

Using IQ as an example: if you decide to answer a question because it excites you and someone else hasn’t already given a similar answer, then your answer is probably not ego driven. But if upon reading the answers, you’re convinced that they're all wrong and you want to prove it (rather than offer a different perspective) with your answer, then your answer is probably ego driven.

I notice that you asked:
"How do you know if a desire is ego driven?”
and not
“How do you know if a desire originates from ego?”

Isn't every desire that comes into one's awareness and is acted upon, whether it's a desire that originates from an ego perspective or a desire that originates from a spiritual (higher self) perspective, ultimately, wanted by our ego?

Put another way, regardless of where the desire originates from, isn't it still within the domain of one's ego to either accept and act upon that desire or to simply reject it? Even if a desire causes one to seemingly do good for others at the expense of oneself, it's still a choice made by one's ego. Is it not?

Does the desire benefit you at the cost of others or does the desire benefit others at the cost of you?

This is the simple way to tell if it is Ego driven or if it is Divine driven. The Ego is all about the self while the Holy Spirit is all about others.

Ego is always present. Ego is self-esteem. Even when self-esteem is at it's lowest, it's still there.