1) Change the layer name(s) in ArcMap, and either delete, republish or update the service definition.
2) Go to the service URL for the feature service, and change the URL to access the Admin section (http://services.arcgis.com/[Org code]/ArcGIS/rest/admin/services/[Service name]/FeatureServer).
3. Click the layer to be renamed > Update Definition > Search for the layer name, and rename the layer.
4. Search for 'LastEditDate', and change the number to "null" (without quotes) > Update Service Definition.