Depending on where you want it, it could be just a simple template edit (such a post) or you'll have use hooks to pull in the userfield in other places that don't normally fetch it when displaying username.
As was said this is simple if you only want this to show in the postbit... more complicated but not impossible if you want it elsewhere... but it may get confusing because if people need to use PM's they would have to send them to their username, not display name... also 'quotes' may be an issue quoted by username by default.