public string DisplayField {get; set;}

{
    // get the CIM definition from the layer
    // Note: needs to be called on the MCT
    var cimFeatureDefinition = featureLayer.GetDefinition() as ArcGIS.Core.CIM.CIMBasicFeatureLayer;
    // get the view of the source table underlying the layer
    var cimDisplayTable = cimFeatureDefinition.FeatureTable;
    // this field is used as the 'label' to represent the row
    var displayField = cimDisplayTable.DisplayField;
}