Southpaw has very little meaning to the movie. "Hope" is perfect since it's the main charcater's last name...In fact would even have consider to name it "Billy Hope". It would have made the character more memorable (Rocky, Forrest Gump, etc). I think Gyllenhaal's acting deserved it.
Honestly, I think Southpaw is a great name for this movie. Going southpaw during the final match was how he took revenge on Escobar for the murder on Maureen, and going southpaw changed his life back for the better. Besides, it's a more original title than his name Hope. If the movie was titled Hope, you wouldn't have a clue as to what's it about and if you hear Southpaw, you want to know what it's about because many people don't know the word. But thats just my opinion :)
'a walk to remember' is never explained in its own movie. you have to read the book to get it. (yeah i just proved i'm a girl) there's plenty of movies where the title makes no sense with the rest of the movie.
I think it's called Southpaw not just because it was the punch that won him the title, but also because using it changed up his boxing routine, and metaphorically it was changing up his life that brought him back victory.