According to the PMBOK® Guide and the Standard for Project Management, the process described is Control Costs. This process falls under the Monitoring and Controlling Process Group and the Project Cost Management Knowledge Area.

The primary purpose of Control Costs is to maintain the cost baseline throughout the project. According to PMI standards, this process involves:

Monitoring the status of the project: Tracking actual costs incurred against the planned budget.

Updating project costs: Incorporating actual costs and revised estimates into the project records.

Managing changes to the cost baseline: Ensuring that all changes to the baseline are processed through the Perform Integrated Change Control process.

Informing stakeholders: Reporting cost-related changes and variances that may affect the budget.

The other options are incorrect based on their specific definitions in the Project Cost Management Knowledge Area:

Plan Cost Management: This is the process of defining how the project costs will be estimated, budgeted, managed, monitored, and controlled. It creates the framework, but does not perform the monitoring.

Estimate Costs: This is the process of developing an approximation of the monetary resources needed to complete project work. It occurs during the Planning phase.

Determine Budget: This is the process of aggregating the estimated costs of individual activities or work packages to establish an authorized cost baseline.

As per the PMI Lexicon of Project Management Terms, the key benefit of the Control Costs process is that it provides the means to recognize variance from the plan in order to take corrective action and minimize risk.