Final answer:
Azure Cost Management is the feature that lets you set cost alerts and manage budgets in Azure, including monitoring and optimizing costs.
Step-by-step explanation:
The feature that allows you to set cost alerts is Azure Cost Management. This service provides tools to monitor, manage, and optimize costs across Azure services. With Azure Cost Management, you can create and manage budgets, track spending against your budgets, and set up alerts to be notified when your spending reaches or approaches the threshold you define.
It integrates with Azure Cost Analysis for in-depth analysis of your spending patterns and potential savings.