Salesforce Error 'Duplicate label' When Deploying Global Picklist Value Set

The "Duplicate label" error when attempting to deploy a Change Set that includes a Global Picklist Value Set with changes to its Picklist value API names is considered expected behavior.

When deploying changes to Picklist values via Change Sets, the system will look at the Picklist value's API name as its unique identifier. So if one attempts to change just the picklist value's Label, the system will recognize the value based on its API name and make the change.

However, if one tries to change the API name itself, the system will think that the intent is to try to create a new Picklist value, recognize that there's already a value in the system with the same label, and throw the duplicate label error.