尝试等待API调用：

List<string> currentTables = await client.ListTablesAsync().Result.TableNames;
            MessageBox.Show(currentTables.Count.ToString());

请尝试使用此同步代码：

AmazonDynamoDBClient client = new AmazonDynamoDBClient();

// Initial value for the first page of table names.
string lastEvaluatedTableName = null;
do
{
   // Create a request object to specify optional parameters.
   var request = new ListTablesRequest
   {
     Limit = 10, // Page size.
     ExclusiveStartTableName = lastEvaluatedTableName
   };

   var response = client.ListTables(request);
   ListTablesResult result = response.ListTablesResult;
   foreach (string name in result.TableNames)
     Console.WriteLine(name);

   lastEvaluatedTableName = result.LastEvaluatedTableName;

} while (lastEvaluatedTableName != null);