In S. E. Hinton's The Outsiders, what are some events that show how Ponyboy struggles with his identity, but ultimately, remains true to himself?

Pony worries about being a greaser, but he finds a way to be true to his friends and still sensitive and intelligent. 

Pony explains early on that he is not like the other greasers, but he still feels a deep connection to them.  He is not a fighter, and not a high school dropout.  He is more sensitive and considered deeper than the others. They care about him and want him to follow his ambitions. 

I'm supposed to be smart; I make good grades and have a high IQ and everything, but I don't use my head. Besides, I like walking. (Ch. 1) 

So Pony often seems different from the other greasers.  For example, when Two-bit hands him a broken bottle when the Socs drive by, he says he would never use it.  The other greasers feel like Pony is a little more delicate and inside his head. 

Yet Pony does fight when he needs to.   He participates in the rumble, even though he is still recovering from his injuries from the fire.  He wants to do it because he wants to support his greaser friends.  

"Ponyboy, listen, don't get tough. You're not like the rest of us and don't try to be..."

What was the matter with Two-Bit? I knew as well as he did that if you got tough you didn't get hurt. Get smart and nothing can touch you... (Ch. 12) 

He survives, again with an injury.  He does feel proud of himself for participating.  He feels like he is pulling his own weight.  He also likes the fact that the greasers won.  It makes him proud. 

Johnny tells Pony to stay gold.  He wants him to stay in school and get an education. The other greasers, especially his Brother Darry, agree.  They know that Pony has a chance to make something of himself.