How do I explain faith and identity it as a theme in the film The Green Mile?

It might not be a bad idea to consider collapsing both of the ideas into one theme.  Faith is a critical part to individual identity in the Darabont's film.  On one hand, Paul is forced to accept Coffey's powers on faith, helping to add a new dimension to his patterned and sequence based identity.  The faith that Paul learns as a result of his work with Coffey helps to bring to light what it means to possess a complex identity.  In this light, faith and identity go together, as one where the former enhances the latter.  Paul's identity as person and professional is furthered greatly as a result of his faith in John Coffey.  At the same time, outliving everyone else is a result of his faith in what John did and helps to develop his identity of both his own sense of self and what "the Green Mile" actually is in a setting outside of prison.  Faith has become a critical part of Paul's life and identity, though it might not be a liberating vision.