In Fallen Angels, which character searched for and arrived at a sense of identity?Please explain what led this particular character to arrive at...

In all actuality, all of the men on Perry's squad are searching for a sense of identity, and most of them who remain living at the end of the novel arrive at a sense of identity.  Here are several examples.

--Perry: The novel is, of course, mainly about Perry's growth and recognition of self.  Perry joins the military because he just does not know what else to do.  His mother and brother desperately need money for basic necessities; so the military enables Perry to provide for those needs.  Perry is certainly intelligent enough to go to college but just doesn't see a way to make that possible while providing for his brother Kenny and his own needs such as clothing.  While deployed to Vietnam, Perry begins to think about why he is in the country, what the war is about, and what his purpose is in life.  While he does come to the conclusion that no one seems to know what they're doing in Vietnam, he also realizes that he has developed lasting relationships with his squad members and that he would do anything for them.  On the plane ride home, Perry thinks of the men whom he befriended in combat and has a feeling of being able to accomplish anything now that he has made it through combat.

--Peewee: Perry's best friend jokes about the joining the military because he was dared to, but once he is in the Army, he recognizes that it is the first time that he is treated equally--he has the same as everyone else, and he likes that treatment.  Even though Peewee cracks jokes through most of the novel, after his near-death experience with Perry in the spider hole, he realizes that life is important to him and that he wants to settle down and be able to accomplish something back in the "world."

--Johnson: Big Johnson enlisted because he couldn't find a job as an African American living in the South.  Similar to Peewee, the military provides a way for Johnson to escape his environment.  Even though he does not say much through the novel, Johnson commands respect (This is probably the first time in his life that he realizes his ability to do so.). At the end of the novel, he is still out in the "boonies" with the squad, but he has acquired the confidence that he needs to recognize his leadership abilities.