diff --git a/src/backend/catalog/heap.c b/src/backend/catalog/heap.c
index fd6537567ea..5b558f30c7a 100644
--- a/src/backend/catalog/heap.c
+++ b/src/backend/catalog/heap.c
@@ -2635,6 +2635,7 @@ AddRelationNewConstraints(Relation rel,
 			 * requested validity.
 			 */
 			if (AdjustNotNullInheritance(RelationGetRelid(rel), colnum,
+										 cdef->conname,
 										 is_local, cdef->is_no_inherit,
 										 cdef->skip_validation))
 				continue;
diff --git a/src/backend/catalog/pg_constraint.c b/src/backend/catalog/pg_constraint.c
index 2d5ac1ea813..afdfac8eca6 100644
--- a/src/backend/catalog/pg_constraint.c
+++ b/src/backend/catalog/pg_constraint.c
@@ -731,14 +731,15 @@ extractNotNullColumn(HeapTuple constrTup)
  * If a constraint exists but the connoinherit flag is not what the caller
  * wants, throw an error about the incompatibility.  If the desired
  * constraint is valid but the existing constraint is not valid, also
- * throw an error about that (the opposite case is acceptable).
+ * throw an error about that (the opposite case is acceptable).  If
+ * the proposed constraint has a different name, also throw an error.
  *
  * If everything checks out, we adjust conislocal/coninhcount and return
  * true.  If is_local is true we flip conislocal true, or do nothing if
  * it's already true; otherwise we increment coninhcount by 1.
  */
 bool
-AdjustNotNullInheritance(Oid relid, AttrNumber attnum,
+AdjustNotNullInheritance(Oid relid, AttrNumber attnum, const char *new_conname,
 						 bool is_local, bool is_no_inherit, bool is_notvalid)
 {
 	HeapTuple	tup;
@@ -777,6 +778,22 @@ AdjustNotNullInheritance(Oid relid, AttrNumber attnum,
 					errhint("You might need to validate it using %s.",
 							"ALTER TABLE ... VALIDATE CONSTRAINT"));
 
+		/*
+		 * If, for a new constraint that is being defined locally (i.e., not
+		 * being passed down via inheritance), a name was specified, then
+		 * verify that the existing constraint has the same name.  Otherwise
+		 * throw an error.  Names of inherited constraints are ignored because
+		 * they are not directly user-specified, so matching is not important.
+		 */
+		if (is_local && new_conname &&
+			strcmp(new_conname, NameStr(conform->conname)) != 0)
+			ereport(ERROR,
+					errcode(ERRCODE_OBJECT_NOT_IN_PREREQUISITE_STATE),
+					errmsg("cannot create not-null constraint \"%s\" on column \"%s\" of table \"%s\"",
+						   new_conname, get_attname(relid, attnum, false), get_rel_name(relid)),
+					errdetail("A not-null constraint named \"%s\" already exists for this column.",
+							  NameStr(conform->conname)));
+
 		if (!is_local)
 		{
 			if (pg_add_s16_overflow(conform->coninhcount, 1,
diff --git a/src/include/catalog/pg_constraint.h b/src/include/catalog/pg_constraint.h
index 4afceb5c692..3a03b8d801a 100644
--- a/src/include/catalog/pg_constraint.h
+++ b/src/include/catalog/pg_constraint.h
@@ -263,7 +263,7 @@ extern HeapTuple findNotNullConstraintAttnum(Oid relid, AttrNumber attnum);
 extern HeapTuple findNotNullConstraint(Oid relid, const char *colname);
 extern HeapTuple findDomainNotNullConstraint(Oid typid);
 extern AttrNumber extractNotNullColumn(HeapTuple constrTup);
-extern bool AdjustNotNullInheritance(Oid relid, AttrNumber attnum,
+extern bool AdjustNotNullInheritance(Oid relid, AttrNumber attnum, const char *new_conname,
 									 bool is_local, bool is_no_inherit, bool is_notvalid);
 extern List *RelationGetNotNullConstraints(Oid relid, bool cooked,
 										   bool include_noinh);
diff --git a/src/test/regress/expected/constraints.out b/src/test/regress/expected/constraints.out
index 1bbf59cca02..ebc892a2a42 100644
--- a/src/test/regress/expected/constraints.out
+++ b/src/test/regress/expected/constraints.out
@@ -846,8 +846,12 @@ CREATE TABLE notnull_tbl1 (a INTEGER NOT NULL NOT NULL);
 Not-null constraints:
     "notnull_tbl1_a_not_null" NOT NULL "a"
 
--- no-op
+-- specifying an existing constraint is a no-op
+ALTER TABLE notnull_tbl1 ADD CONSTRAINT notnull_tbl1_a_not_null NOT NULL a;
+-- but using a different constraint name is not allowed
 ALTER TABLE notnull_tbl1 ADD CONSTRAINT nn NOT NULL a;
+ERROR:  cannot create not-null constraint "nn" on column "a" of table "notnull_tbl1"
+DETAIL:  A not-null constraint named "notnull_tbl1_a_not_null" already exists for this column.
 \d+ notnull_tbl1
                                Table "public.notnull_tbl1"
  Column |  Type   | Collation | Nullable | Default | Storage | Stats target | Description 
diff --git a/src/test/regress/sql/constraints.sql b/src/test/regress/sql/constraints.sql
index 733a1dbccfe..1e9989698b6 100644
--- a/src/test/regress/sql/constraints.sql
+++ b/src/test/regress/sql/constraints.sql
@@ -623,7 +623,9 @@ DROP TABLE deferred_excl;
 -- verify constraints created for NOT NULL clauses
 CREATE TABLE notnull_tbl1 (a INTEGER NOT NULL NOT NULL);
 \d+ notnull_tbl1
--- no-op
+-- specifying an existing constraint is a no-op
+ALTER TABLE notnull_tbl1 ADD CONSTRAINT notnull_tbl1_a_not_null NOT NULL a;
+-- but using a different constraint name is not allowed
 ALTER TABLE notnull_tbl1 ADD CONSTRAINT nn NOT NULL a;
 \d+ notnull_tbl1
 -- duplicate name