public string GetName()

public async Task ObtainingDefinitionsFromGeodatabase()
{
  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(
      new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
    {
      var enterpriseDefinitions = 
        geodatabase.GetDefinitions<FeatureClassDefinition>();
      IEnumerable<Definition> featureClassesHavingGlobalID = 
        enterpriseDefinitions.Where(definition => definition.HasGlobalID());

      var featureDatasetDefinitions = 
        geodatabase.GetDefinitions<FeatureDatasetDefinition>();
      bool electionRelatedFeatureDatasets = 
        featureDatasetDefinitions.Any(
          definition => definition.GetName().Contains("Election"));

      var attributedRelationshipClassDefinitions = 
        geodatabase.GetDefinitions<AttributedRelationshipClassDefinition>();

      var relationshipClassDefinitions = 
        geodatabase.GetDefinitions<RelationshipClassDefinition>();
    }
  });
}