1. HashiCorp Terraform Documentation, "Provider Requirements":
Location: Configuration Language -> Providers -> Provider Requirements.
Quote: "The requiredproviders block specifies all of the providers required by the current module, mapping each local provider name to a source address and a version constraint. The local name is used in the rest of the configuration to refer to the provider..." This text explicitly states that the local name is used throughout the rest of the configuration.
URL: https://developer.hashicorp.com/terraform/language/providers/requirements
2. HashiCorp Terraform Documentation, "Providers":
Location: Configuration Language -> Providers.
Quote: "A provider block configures a specified provider, such as aws. A provider is a plugin that Terraform uses to create and manage your resources... To configure a particular provider, you can use a provider block. This block is identified by the local name of the provider it configures." This confirms that the provider configuration block itself is identified by the local name.
URL: https://developer.hashicorp.com/terraform/language/providers/configuration
3. HashiCorp Learn, "Manage Providers" Tutorial:
Location: Terraform -> Tutorials -> Manage Providers.
Quote: "Terraform uses the provider's local name when you reference it in your configuration, for example when you define a resource. In this case, the local name for the hashicorp/random provider is random." This tutorial reinforces the concept by providing a clear example of the mapping between the source (hashicorp/random) and the local name (random) and its subsequent use in resource definitions.
URL: https://developer.hashicorp.com/terraform/tutorials/configuration-language/providers#review-provider-configuration