You can submit a Name Split. It depends on which credits belong to you and which ones belong to the other person and in which categories.
For example, If all the titles in the Composers and Music Department belongs to you and the titles in the titles in the other categories do not, then you would submit a Name Split for the other categories. which will move the credits to a new name page with a different Roman numeral.
However, if your credits and the other person's credits are listed in the same category, then you would need to submit a Name Correction to move at least one of the credits to the new name page. After that update has been processed, then you can move any other credits to the correct name page.
I hope this helps. Please write back if you need some assistance with the update.