Get the list of snapshots using VMWareTasks.

snapshot_names.cs

private List<string> GetSnapshotNames(IEnumerable<VMWareSnapshot> snapshots)
{
  List<string> result = new List<string>();
  foreach (VMWareSnapshot snapshot in snapshots)
  {
    result.Add(snapshot.DisplayName);
    result.AddRange(GetSnapshotNames(snapshot.ChildSnapshots));
  }
  return result;
}

List<string> snapshotNames = GetSnapshotNames(virtualMachine.Snapshots);