Is there an option to remove duplicate polygon labels in QGIS?

For polygons, there is an option called "label every part of multi-part features" in advanced labeling settings. Consequently, it is possible to label only one part of a multi-part feature.

If I understand you correctly, your dataset contains multiple polygon features with same labels but the are NOT part of one multi-part feature.

Therefore, you'll have to merge these single-part features into multi-part features based on the label attribute: Vector - Geometry tools - Singleparts to multipart (in later versions this tool is named 'Collect Geometries').

Check also if you are using the old labelling engine (the one still available in the vector properties) or if you are using the new labelling engine, available through a button in the toolbar (the icon has the letters "abc" underlined with a blue line). The new engine is much better than the old and there is more control on how/what labels draw.