Because of how vector-tiles work, you'll actually have to calculate the label locations yourself as a separate point layer. This should be pretty easy to do w/ any GIS program like qGIS/ArcGIS/PostGIS by calculating the centroid of each polygon, doing a spatial join to save the polygon label to the corresponding centroid point, and saving the result as a new point shp file.
Upload the result to MB, import it into your project and add labels via the new point layer, rather than the polygon layer.
The reason this is necessary is b/c vector-tiles actually split your polygons into tiles. Sufficiently large polygons will actually be cut into multiple polygons, so calculating polygon centroids on tiled polygons doesn't really make sense.
(by the way, I'm assuming you're using the new web-based MapBox Studio, not MapBox Studio Classic -- the answer is essentially the same either way, except that with the latter, you'd import the new label-point layer into your local download of MB Studio Classic, rather than uploading to your MB account).