Can Legal First and Last Name Be Captured in RMI After Offer Acceptance (ORC) and Mapped to Core HR?

We have a business requirement to capture candidate's Legal First Name and Legal Last Name after the offer process is completed using the RMI.

The requirement is to present mandatory questions in RMI for candidates to enter their Legal First Name and Legal Last Name, and then have these values automatically update the corresponding Legal Name fields in the Core HR person record.