why Esther did not reveal her identity right away

When Mordechai told Esther to go to Achashveirosh to plead on behalf of the Jewish people, she replied that she had not been called to the king for thirty day.  Anyone who appeared before the king without being called risked being killed (4:11). Mordechai responded by reiterating his demand that Esther go, as the Jewish people were in grave danger. Was Esther really more concerned for her personal safety than the plight of the nation? Of course not. The Vilna Gaon explains that Esther was telling Mordechai that precisely because she had not been called into an audience with the king in thirty days, therefore, the king was bound to call her in sometime very soon. She was not trying to avoid carrying out Mordechai's mission -- she was telling Mordechai that if he would only wait a short time she could carry out that mission with no danger to herself.

Why then did Mordechai demand that she act immediately? R' Chaim Kaneivsky in his Ta'ama d'Kra explains the Mordechai held that the fear and stress caused by the impending danger was itself a life threatening. Living in a precarious situation can cause a person to collapse. Therefore, Esther needed to act immediately.

I don't want to get bogged down in current events, but history does repeat itself. With respect to Iran's nuclear weapon threat, we hear voices saying to just wait some time before acting -- give economic sanctions (which have not worked until now) time to work, give diplomacy (which has accomplished nothing until now) a chance, etc. These voices fail to appreciate that living with danger is itself dangerous. Even if someone knows that the trigger won't be pulled until some point in the future, no person can stand by calmly and idly while a maniac waves a gun at his/her head without going crazy from nervous tension.

Returning to the megillah, the truth is that Esther did not act right away. Despite the fact that she now understood the immediacy of the danger, Esther still delayed for three days during which time Mordechai and Klal Yisrael fasted and davened with her. A very important yesod: Sakanah does not demand any action be taken in response -- it demands effective action that will eliminate or mitigate the danger. Action without tefilah, without first asking Hashem for help, is guaranteed to not be effective.

So I take back the first sentence of the previous paragraph. Esther did act immediately to reduce the danger, as the first and most important step in any crisis is to be mispallel.  That set the wheels of her success in motion, as it triggered the needed siyata d'shemaya.

And this too applies to current events as well...

Since I mentioned R' Chaim Kanievsky's Ta'ama d'Kra, I want to point out what seems to me to be a remarkable chiddush that he says. There are various reasons offered in the commentaries as to why Mordechai told Esther not to reveal that she was a member of Klal Yisrael. R' Chaim suggests as follows: Were Esther's nationality to be known, no one would dare act against her or her people and Haman's plot would never have gotten off the ground.  Now, you or I might think this is a great thing, but that's why you and I are not Mordechai.  Mordechai knew that Klal Yisrael deserved to be punished for their having partaken of Achashveirosh's party. If Haman's plot or some other plot never stood a chance, then the punishment for Klal Yisrael would come purely b'ydei shamayim, at the hands of Hashem through midas ha'din.  Mordechai figured that it is better to allow some plot to develop, better to allow Haman the chance to put Klal Yisrael in danger (and then to undo that danger), than to foil that effort and risk punishment b'ydei shamayim.  Haman's decree amounted to the lesser of two evils.