If there is a user with completed courses against a specific username and I want to change the username, will that invalidate the completed course(meaning the course will need to be taken again) or simply transfer the completed course to the new username?
As long as you edit the username within the existing user profile, it will keep all the records with the new username with no other side effects.
Bridge keeps a set of records associated with a specific user ID. The system doesn't really care what the username is to log into that user ID. The username can change all it wants and it just points to the same user ID when the person logs in.
I've had to do this quite often. My company uses people's email address as their username/UID. When a person gets married and changes their name, they often get IT to change their email to their married name. When they do that, I just change their username/UID in Bridge to match the new email so when the system syncs with the HRIS, it now syncs with the same account but under a new username/UID.