@Test
  public void testTableName() {
    Schema schema = getTestSchema();
    PartitionSpec spec = PartitionSpec.builderFor(schema).bucket("data", 16).build();
    TableIdentifier tableIdent = TableIdentifier.of(DB_NAME, "tbl");

    try {
      catalog.buildTable(tableIdent, schema)
          .withPartitionSpec(spec)
          .create();

      Table table = catalog.loadTable(tableIdent);
      assertThat(table.name()).as("Name must match").isEqualTo("hive.hivedb.tbl");

      TableIdentifier snapshotsTableIdent = TableIdentifier.of(DB_NAME, "tbl", "snapshots");
      Table snapshotsTable = catalog.loadTable(snapshotsTableIdent);
      assertThat(snapshotsTable.name())
          .as("Name must match")
          .isEqualTo("hive.hivedb.tbl.snapshots");
    } finally {
      catalog.dropTable(tableIdent);
    }
  }
Run all the tests from abstract of {@link CatalogTests} with few specific tests related to HIVE.
iceberg/iceberg-catalog/src/test/java/org/apache/iceberg/hive/TestHiveCatalog.java