diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 87bc688704..68b62d523d 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -5368,13 +5368,14 @@ add_guc_variable(struct config_generic *var, int elevel)
 /*
  * Decide whether a proposed custom variable name is allowed.
  *
- * It must be "identifier.identifier", where the rules for what is an
- * identifier agree with scan.l.
+ * It must be two or more identifiers separated by dots, where the rules
+ * for what is an identifier agree with scan.l.  (If you change this rule,
+ * adjust the errdetail in find_option().)
  */
 static bool
 valid_custom_variable_name(const char *name)
 {
-	int			num_sep = 0;
+	bool		saw_sep = false;
 	bool		name_start = true;
 
 	for (const char *p = name; *p; p++)
@@ -5383,7 +5384,7 @@ valid_custom_variable_name(const char *name)
 		{
 			if (name_start)
 				return false;	/* empty name component */
-			num_sep++;
+			saw_sep = true;
 			name_start = true;
 		}
 		else if (strchr("ABCDEFGHIJKLMNOPQRSTUVWXYZ"
@@ -5400,8 +5401,8 @@ valid_custom_variable_name(const char *name)
 	}
 	if (name_start)
 		return false;			/* empty name component */
-	/* OK if we had exactly one separator */
-	return (num_sep == 1);
+	/* OK if we found at least one separator */
+	return saw_sep;
 }
 
 /*
@@ -5516,7 +5517,7 @@ find_option(const char *name, bool create_placeholders, bool skip_errors,
 						(errcode(ERRCODE_INVALID_NAME),
 						 errmsg("invalid configuration parameter name \"%s\"",
 								name),
-						 errdetail("Custom parameter names must be of the form \"identifier.identifier\".")));
+						 errdetail("Custom parameter names must be two or more simple identifiers separated by dots.")));
 			return NULL;
 		}
 	}
diff --git a/src/test/regress/expected/guc.out b/src/test/regress/expected/guc.out
index c55871a972..59da91ff04 100644
--- a/src/test/regress/expected/guc.out
+++ b/src/test/regress/expected/guc.out
@@ -515,6 +515,8 @@ SET no_such_variable TO 42;
 ERROR:  unrecognized configuration parameter "no_such_variable"
 -- Test "custom" GUCs created on the fly (which aren't really an
 -- intended feature, but many people use them).
+SHOW custom.my_guc;  -- error, not known yet
+ERROR:  unrecognized configuration parameter "custom.my_guc"
 SET custom.my_guc = 42;
 SHOW custom.my_guc;
  custom.my_guc 
@@ -522,14 +524,28 @@ SHOW custom.my_guc;
  42
 (1 row)
 
+RESET custom.my_guc;  -- this makes it go to empty, not become unknown again
+SHOW custom.my_guc;
+ custom.my_guc 
+---------------
+ 
+(1 row)
+
+SET custom.my.qualified.guc = 'foo';
+SHOW custom.my.qualified.guc;
+ custom.my.qualified.guc 
+-------------------------
+ foo
+(1 row)
+
 SET custom."bad-guc" = 42;  -- disallowed because -c cannot set this name
 ERROR:  invalid configuration parameter name "custom.bad-guc"
-DETAIL:  Custom parameter names must be of the form "identifier.identifier".
+DETAIL:  Custom parameter names must be two or more simple identifiers separated by dots.
 SHOW custom."bad-guc";
 ERROR:  unrecognized configuration parameter "custom.bad-guc"
 SET special."weird name" = 'foo';  -- could be allowed, but we choose not to
 ERROR:  invalid configuration parameter name "special.weird name"
-DETAIL:  Custom parameter names must be of the form "identifier.identifier".
+DETAIL:  Custom parameter names must be two or more simple identifiers separated by dots.
 SHOW special."weird name";
 ERROR:  unrecognized configuration parameter "special.weird name"
 --
diff --git a/src/test/regress/sql/guc.sql b/src/test/regress/sql/guc.sql
index 3650188d9d..c39c11388d 100644
--- a/src/test/regress/sql/guc.sql
+++ b/src/test/regress/sql/guc.sql
@@ -151,8 +151,13 @@ SET no_such_variable TO 42;
 
 -- Test "custom" GUCs created on the fly (which aren't really an
 -- intended feature, but many people use them).
+SHOW custom.my_guc;  -- error, not known yet
 SET custom.my_guc = 42;
 SHOW custom.my_guc;
+RESET custom.my_guc;  -- this makes it go to empty, not become unknown again
+SHOW custom.my_guc;
+SET custom.my.qualified.guc = 'foo';
+SHOW custom.my.qualified.guc;
 SET custom."bad-guc" = 42;  -- disallowed because -c cannot set this name
 SHOW custom."bad-guc";
 SET special."weird name" = 'foo';  -- could be allowed, but we choose not to