To effectively manage the merging of duplicate account records in Salesforce, which also have associated contacts with the same name, the correct sequence of steps is:

**D. Merge the duplicate accounts and then merge the duplicate contacts.**

Here's the rationale for this approach:

1. **Merge the Duplicate Accounts First**: Merging the accounts first is crucial because it simplifies the subsequent steps by consolidating all related records (like opportunities, contacts, etc.) under a single account. Salesforce allows you to merge up to three duplicate accounts at one time. During this process, you can choose which account to retain as the master record and what specific field values should be preserved.

2. **Then Merge the Duplicate Contacts**: After the accounts are merged, you should then proceed to merge the contacts. Since each account had a contact with the same name, these contacts might now be linked to the newly merged account, depending on your configuration and the specifics of the record linkage. Merging the contacts ensures that there are no redundant contact records in the system, which helps maintain clean data and reduces confusion.

Here’s why the other options are less appropriate:

- **A. Merge the duplicate contacts and then merge the duplicate accounts.**
- This approach could complicate the process because merging contacts first does not address the hierarchical nature of account and contact relationships in Salesforce. Accounts serve as a parent record to contacts, so it’s generally more logical and systematic to start merging at the account level.

- **B. Merge the duplicate accounts and check the box that optionally merges the duplicate contacts.**
- While this option sounds convenient, Salesforce does not actually offer an automatic "check a box" option to merge contacts while merging accounts. Each type of record (accounts, contacts) must be merged separately through their respective merge interfaces.

- **C. Merge the duplicate...

Should be D