[breaking] Save booster feature info in JSON, remove feature name generation. (#6605)

* Save feature info in booster in JSON model.
* [breaking] Remove automatic feature name generation in `DMatrix`.

This PR is to enable reliable feature validation in Python package.

tests/cpp/test_learner.cc

@@ -360,4 +360,60 @@ TEST(Learner, ConstantSeed) {
     CHECK_EQ(v_0, v_2);
   }
 }
+
+TEST(Learner, FeatureInfo) {
+  size_t constexpr kCols = 10;
+  auto m = RandomDataGenerator{10, kCols, 0}.GenerateDMatrix(true);
+  std::vector<std::string> names(kCols);
+  for (size_t i = 0; i < kCols; ++i) {
+    names[i] = ("f" + std::to_string(i));
+  }
+
+  std::vector<std::string> types(kCols);
+  for (size_t i = 0; i < kCols; ++i) {
+    types[i] = "q";
+  }
+  types[8] = "f";
+  types[0] = "int";
+  types[3] = "i";
+  types[7] = "i";
+
+  std::vector<char const*> c_names(kCols);
+  for (size_t i = 0; i < names.size(); ++i) {
+    c_names[i] = names[i].c_str();
+  }
+  std::vector<char const*> c_types(kCols);
+  for (size_t i = 0; i < types.size(); ++i) {
+    c_types[i] = names[i].c_str();
+  }
+
+  std::vector<std::string> out_names;
+  std::vector<std::string> out_types;
+
+  Json model{Object()};
+  {
+    std::unique_ptr<Learner> learner{Learner::Create({m})};
+    learner->Configure();
+    learner->SetFeatureNames(names);
+    learner->GetFeatureNames(&out_names);
+
+    learner->SetFeatureTypes(types);
+    learner->GetFeatureTypes(&out_types);
+
+    ASSERT_TRUE(std::equal(out_names.begin(), out_names.end(), names.begin()));
+    ASSERT_TRUE(std::equal(out_types.begin(), out_types.end(), types.begin()));
+
+    learner->SaveModel(&model);
+  }
+
+  {
+    std::unique_ptr<Learner> learner{Learner::Create({m})};
+    learner->LoadModel(model);
+
+    learner->GetFeatureNames(&out_names);
+    learner->GetFeatureTypes(&out_types);
+    ASSERT_TRUE(std::equal(out_names.begin(), out_names.end(), names.begin()));
+    ASSERT_TRUE(std::equal(out_types.begin(), out_types.end(), types.begin()));
+  }
+}
 }  // namespace xgboost