When using the Rename Tabs and Labels option in Salesforce, you can rename the tabs and labels on any of the objects listed.

In this example I rename the Description Label on Case from Description to This is the label I have renamed from Description.

Renaming the label using this method also bypasses the maximum restriction of 40 characters that Salesforce has on these fields.

This renaming then shows against the object in Salesforce.

When deploying this Standard Object with Gearset (Case.Description in this instance), the change in the label will not show against the custom object itself and the label field will not be pulled for the object over the metadata api.

If no other changes have been made to the object, the object will show as no difference in a comparison.

To see the new label, the CustomObjectTranslation metadata type needs to be included in your metadata filter along with the CustomObject metadata type.

The label name change will then show in your comparison as a Custom object translation, which can be selected and deployed to your target.

In this example, this shows as Case-en_US