IMHO - yes. With security checking boarding passes and drivers licenses, I would make sure you change it. However, I think SW is reasonable about this. I made a mistake last Dec with my DS - I put her maiden name as her last name (if you knew my DBIL - maybe it was wishful thinking). Anyway, I didn't realize the mistake until I had PRINTED the boarding passes!!!!! I was next to tears and in a MAJOR panic. I called them and they were great. They said it would have been easier if I had not printed the passes, but we still got it straightened out.
My advice - call them NOW and get the change made. I bet they'll be nice about it and you won't have to worry.
Let us know how it goes!!!