I have a student whose name changed mid-semester, and the change has been made on the LMS.
The result is that on WeBWorK, they've completed Homeworks 1-5 under one name, and 6-current under another.
Is there any way to handle this, other than manually merging the scores at the end?
I think merging the scores at the end is the simplest solution. Unfortunately the database uses the user name as a primary key so it's not easy to change a user name or combine two user's scores. You could do it with direct access to the database, but unless there are a lot of students involved I don't think it would be worth the trouble.