I have not named her so far.

Some people name their hawks, and others do not.

If they call their hawks to their arms, then they do it by whistling.

So even if they name their hawks, they do not call them by their names.

At least so far I have not seen anyone, who would call their hawk to his/her arm by the name of their bird.

Maybe it is possible, maybe not.
Maybe it is depending on the bird.

Every bird is an individual with different personalities. Just like people.