public IReadOnlyList<string> GetStyleNames()

var serverConnection = new CIMInternetServerConnection { URL = "https://spritle.esri.com/arcgis/services/sanfrancisco_sld/MapServer/WMSServer" };
var connection = new CIMWMSServiceConnection { ServerConnection = serverConnection };
LayerCreationParams parameters = new LayerCreationParams(connection);
parameters.MapMemberPosition = MapMemberPosition.AddToBottom;
await QueuedTask.Run(() =>
{
  var compositeLyr = LayerFactory.Instance.CreateLayer<WMSLayer>(parameters, MapView.Active.Map);
  //wms layer in ArcGIS Pro always has a composite layer inside it
  var wmsLayers = compositeLyr.Layers[0] as ServiceCompositeSubLayer;
  //each wms sublayer belongs in that composite layer
  var highwayLayerWMSSub = wmsLayers.Layers[1] as WMSSubLayer;
  //toggling a sublayer's visibility
  if ((highwayLayerWMSSub != null))
  {
    bool visibility = highwayLayerWMSSub.IsVisible;
    highwayLayerWMSSub.SetVisibility(!visibility);
  }
  //applying an existing style to a wms sub layer
  var pizzaLayerWMSSub = wmsLayers.Layers[0] as WMSSubLayer;
  var currentStyles = pizzaLayerWMSSub.GetStyleNames();
  pizzaLayerWMSSub.SetStyleName(currentStyles[1]);
});