diff --git a/include/openmc/geometry_aux.h b/include/openmc/geometry_aux.h
index 14e119282a..0e694e9825 100644
--- a/include/openmc/geometry_aux.h
+++ b/include/openmc/geometry_aux.h
@@ -46,21 +46,21 @@ namespace openmc {
     auto get_count(int32_t univ);
   };
 
-  struct  LevelCountStorage {
+  struct  UniverseLevelCounter {
   private:
-    LevelCountStorage() {}
-    LevelCountStorage(LevelCountStorage& c) {}
-    LevelCountStorage(const LevelCountStorage& c) {}
+    UniverseLevelCounter() {}
+    UniverseLevelCounter(UniverseLevelCounter& c) {}
+    UniverseLevelCounter(const UniverseLevelCounter& c) {}
 
-    static LevelCountStorage* instance_;
+    static UniverseLevelCounter* instance_;
 
     std::map<int32_t, int> counts;
 
   public:
 
-    static LevelCountStorage* instance() {
+    static UniverseLevelCounter* instance() {
       if (instance_ == nullptr)
-        instance_ = new LevelCountStorage;
+        instance_ = new UniverseLevelCounter;
 
       return instance_;
     }
diff --git a/src/finalize.cpp b/src/finalize.cpp
index 3b8530b212..5343823821 100644
--- a/src/finalize.cpp
+++ b/src/finalize.cpp
@@ -137,7 +137,7 @@ int openmc_reset()
 {
 
   UniverseCellCounter::instance()->clear();
-  LevelCountStorage::instance()->clear();
+  UniverseLevelCounter::instance()->clear();
 
   for (auto& t : model::tallies) {
     t->reset();
diff --git a/src/geometry_aux.cpp b/src/geometry_aux.cpp
index 42fb332844..3a98d02b6d 100644
--- a/src/geometry_aux.cpp
+++ b/src/geometry_aux.cpp
@@ -103,18 +103,18 @@ auto UniverseCellCounter::get_count(int32_t univ) {
     return counts[univ];
 }
 
-void LevelCountStorage::clear() {
+void UniverseLevelCounter::clear() {
   if (instance_ != nullptr) {
     delete instance_;
     instance_ = nullptr;
     }
 }
 
-void LevelCountStorage::set_cell_count_for_univ(int32_t univ, int count) {
+void UniverseLevelCounter::set_cell_count_for_univ(int32_t univ, int count) {
   counts[univ] = count;
 }
 
-void LevelCountStorage::increment_count_for_univ(int32_t univ) {
+void UniverseLevelCounter::increment_count_for_univ(int32_t univ) {
   if (has_count(univ)) {
     counts[univ] += 1;
   } else {
@@ -122,11 +122,11 @@ void LevelCountStorage::increment_count_for_univ(int32_t univ) {
   }
 }
 
-bool LevelCountStorage::has_count(int32_t univ) {
+bool UniverseLevelCounter::has_count(int32_t univ) {
   return counts.count(univ);
 }
 
-void LevelCountStorage::absorb_b_into_a(int32_t a, int32_t b) {
+void UniverseLevelCounter::absorb_b_into_a(int32_t a, int32_t b) {
   if (has_count(a)) {
     counts[a] += counts[b];
   } else {
@@ -134,16 +134,16 @@ void LevelCountStorage::absorb_b_into_a(int32_t a, int32_t b) {
   }
 }
 
-void LevelCountStorage::set_count(int32_t univ, int count) {
+void UniverseLevelCounter::set_count(int32_t univ, int count) {
   counts[univ] = count;
 }
 
-int LevelCountStorage::get_count(int32_t univ) {
+int UniverseLevelCounter::get_count(int32_t univ) {
   return counts[univ];
 }
 
 UniverseCellCounter* UniverseCellCounter::instance_ = nullptr;
-LevelCountStorage* LevelCountStorage::instance_ = nullptr;
+UniverseLevelCounter* UniverseLevelCounter::instance_ = nullptr;
 
 //==============================================================================
 
@@ -626,7 +626,7 @@ distribcell_path(int32_t target_cell, int32_t map, int32_t target_offset)
 int
 maximum_levels(int32_t univ)
 {
-  LevelCountStorage* counter = LevelCountStorage::instance();
+  UniverseLevelCounter* counter = UniverseLevelCounter::instance();
 
   if (counter->has_count(univ)) {
     return counter->get_count(univ);