What are the lessons learned from the theme of identity in Much Ado About Nothing by Shakespeare?

One lesson learned from the theme of identity is that too much of a woman’s identity is tied up in her chastity.  In the seventeenth century, women had no rights.  When Hero is denounced on her wedding day, she dies symbolically.  She has done nothing wrong, but she is rejected by her fiancé and by society.  All of this is on the word of a man who has no proof. 

To reinforce this point for Claudio, the man who allowed himself to be fooled by the callous Don John and ruined Hero’s reputation, we have the funeral scroll. 

CLAUDIO

[Reading out of a scroll]
Done to death by slanderous tongues
Was the Hero that here lies:
Death, in guerdon of her wrongs,
Gives her fame which never dies.
So the life that died with shame
Lives in death with glorious fame.
Hang thou there upon the tomb,
Praising her when I am dumb. (Act 5, Scene 3) 

Claudio marries Hero, but it is not Hero.  He has been told that Hero is dead and he can marry another woman.  When he marries Hero, he will see that it is her.  In doing so, he revives her reputation and she is reborn.  That part is sad, in a way.  She really has no other option than to marry him, and he is the man who did not trust her enough to give her the benefit of the doubt and who humiliated her and renounced her in front of everyone on what was supposed to be her wedding day.

Another lesson learned from Beatrice and Benedick more than Hero and Claudio is that in love you should not settle.  You should find what matters to you and truly makes you happy and go for that.  Both of them claim that they do not want marriage, but they actually enjoy the witty banter of each other's company.  They are the intellectual equals of one another, and for that reason they can see the potential in ending up together.