Create multiple databases dynamically in Microsoft Azure

By using Azure Resource Manager Templates you can reliably deploy the whole infrastructure required by each organisation. So if they need a webserver, database and middleware servers, you can define the whole thing in a template and reliably deploy that for every client.

(from the above link)

• You can deploy, manage, and monitor all of the resources for your solution as a group, rather than handling these resources individually.

• You can repeatedly deploy your solution throughout the development lifecycle and have confidence your resources are deployed in a consistent state.

• You can use declarative templates to define your deployment.

• You can define the dependencies between resources so they are deployed in the correct order.

• You can apply access control to all services in your resource group because Role-Based Access Control (RBAC) is natively integrated into the management platform.

• You can apply tags to resources to logically organize all of the resources in your subscription.

• You can clarify billing for your organization by viewing the rolled-up costs for the entire group or for a group of resources sharing the same tag.

The link above has a lot of resources for learning how to use templates as well as the syntax and usage.

There are a large number of templates at the Azure ARM Template Github page and even some pre-existing templates to get you started deploying SQL Server to Azure (there's also mysql and postgress if you prefer)

Plus many others that you can work through to get accustomed to how they work.

you can use the AZURE SQL Database REST API to do so, its as simple as sending a PUT Request to a URL https://management.azure.com/subscriptions/{subscription-id}/resourceGroups/{resource-group-name}/providers/microsoft.sql/servers/{server-name}/databases/{database-name}?api-version={api-version}

Check out these links for more details

1. https://msdn.microsoft.com/en-us/library/azure/mt163571.aspx
2. https://msdn.microsoft.com/en-us/library/azure/mt163685.aspx