Maybe the title should be Please Write to Me because Leigh really, really wants to be pen pals with Mr. Henshaw. He keeps writing and writing until he gets a response. Leigh wants to be an author, and he's got all this stuff going on inside his head and in his life. So he continues writing to Mr. Henshaw as an outlet and a source of advice. All the chapters are letters that begin "Dear Mr. Henshaw" or diary entries that start out as "Dear Mr. Pretend Henshaw."
The title suggests that Leigh is a boy who wants to communicate and connect, and it gives the reader a lot to think about. Who is this Mr. Henshaw, anyway? He's a distant figure in a way, but through Leigh's letters to him, we see Leigh develop into a real writer and come to terms with his parents' divorce. That's why he gets top billing in the book.