Thank you very much for the explanation!The one with 'craves for' is the only one that is a natural sentence as it stands.
All of them can be used but you need to change the wording for them to be correct.
She really has a desire for recognition, or, she really desires recognition.
She really has a thirst for recognition, or, she really thirst for recognition.
The last one could also be expressed as, She really has a craving for recognition.
They are very similar in meaning but there are nuances. I would say that the order of intensity is desire, thirst, craving, with desire being the weakest.
And according to you which is the one which fits best between the other two sentences?I assume this is a difference between varieties of English. In my variety of English, I would not say "craves for recognition", but "craves recognition".
On the other hand, I might speak of "a craving for recognition".