diff --git a/clang/docs/ReleaseNotes.rst b/clang/docs/ReleaseNotes.rst
--- a/clang/docs/ReleaseNotes.rst
+++ b/clang/docs/ReleaseNotes.rst
@@ -52,6 +52,8 @@
 - Fixes an accepts-invalid bug in C when using a ``_Noreturn`` function
   specifier on something other than a function declaration. This fixes
   `Issue 56800 <https://github.com/llvm/llvm-project/issues/56800>`_.
+- Fix `#56772 <https://github.com/llvm/llvm-project/issues/56772>`_ - invalid
+  destructor names were incorrectly accepted on template classes.
 
 Improvements to Clang's diagnostics
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
diff --git a/clang/lib/Sema/SemaDecl.cpp b/clang/lib/Sema/SemaDecl.cpp
--- a/clang/lib/Sema/SemaDecl.cpp
+++ b/clang/lib/Sema/SemaDecl.cpp
@@ -11496,17 +11496,12 @@
       CXXRecordDecl *Record = Destructor->getParent();
       QualType ClassType = Context.getTypeDeclType(Record);
 
-      // FIXME: Shouldn't we be able to perform this check even when the class
-      // type is dependent? Both gcc and edg can handle that.
-      if (!ClassType->isDependentType()) {
-        DeclarationName Name
-          = Context.DeclarationNames.getCXXDestructorName(
-                                        Context.getCanonicalType(ClassType));
-        if (NewFD->getDeclName() != Name) {
-          Diag(NewFD->getLocation(), diag::err_destructor_name);
-          NewFD->setInvalidDecl();
-          return Redeclaration;
-        }
+      DeclarationName Name = Context.DeclarationNames.getCXXDestructorName(
+          Context.getCanonicalType(ClassType));
+      if (NewFD->getDeclName() != Name) {
+        Diag(NewFD->getLocation(), diag::err_destructor_name);
+        NewFD->setInvalidDecl();
+        return Redeclaration;
       }
     } else if (auto *Guide = dyn_cast<CXXDeductionGuideDecl>(NewFD)) {
       if (auto *TD = Guide->getDescribedFunctionTemplate())
diff --git a/clang/test/SemaCXX/member-class-11.cpp b/clang/test/SemaCXX/member-class-11.cpp
--- a/clang/test/SemaCXX/member-class-11.cpp
+++ b/clang/test/SemaCXX/member-class-11.cpp
@@ -1,4 +1,6 @@
 // RUN: %clang_cc1 -std=c++11 -fsyntax-only -verify %s
+// RUN: %clang_cc1 -std=c++17 -fsyntax-only -verify %s
+// RUN: %clang_cc1 -std=c++20 -fsyntax-only -verify %s
 
 struct rdar9677163 {
   struct Y { ~Y(); };
@@ -6,3 +8,22 @@
   Y::~Y() { } // expected-error{{non-friend class member '~Y' cannot have a qualified name}}
   ~Z(); // expected-error{{expected the class name after '~' to name the enclosing class}}
 };
+
+namespace GH56772 {
+
+template<class T>
+struct A {
+  ~A<T>();
+};
+#if __cplusplus >= 202002L
+// FIXME: This isn't valid in C++20 and later.
+#endif
+
+struct B;
+
+template<class T>
+struct C {
+  ~B(); // expected-error {{expected the class name after '~' to name the enclosing class}}
+};
+
+}