diff --git a/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-always.js b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-always.js
new file mode 100644
index 0000000000..5ae257d8bd
--- /dev/null
+++ b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-always.js
@@ -0,0 +1,16 @@
+// Copyright (C) 2022 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.plaindatetime.prototype.tostring
+description: Show ISO calendar if calendar name is "always"
+features: [Temporal]
+---*/
+
+const dt = new Temporal.PlainDateTime(1976, 11, 18, 15, 23);
+
+assert.sameValue(
+  dt.toString({ calendarName: "always" }),
+  "1976-11-18T15:23:00[u-ca=iso8601]",
+  "shows ISO calendar if calendarName = always"
+);
diff --git a/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-auto.js b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-auto.js
new file mode 100644
index 0000000000..7440f54922
--- /dev/null
+++ b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-auto.js
@@ -0,0 +1,35 @@
+// Copyright (C) 2022 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.plaindatetime.prototype.tostring
+description: Possibly display calendar when calendarName is "auto"
+features: [Temporal]
+---*/
+
+
+const dt = new Temporal.PlainDateTime(1976, 11, 18, 15, 23);
+const customCal = {
+  toString() { return "bogus"; }
+};
+const fakeISO8601Cal = {
+  toString() { return "iso8601"; }
+};
+const expected = "1976-11-18T15:23:00";
+
+assert.sameValue(dt.toString(), expected, "default is calendar = auto (zero arguments)");
+assert.sameValue(dt.toString({ calendarName: "auto" }), expected, "shows only non-ISO calendar if calendarName = auto");
+
+assert.sameValue(
+  dt.withCalendar(fakeISO8601Cal).toString({ calendarName: "auto" }),
+  expected,
+  "Don't show ISO calendar even if calendarName = auto"
+);
+
+const dt2 = new Temporal.PlainDateTime(1976, 11, 18, 15, 23, 0, 0, 0, 0, customCal);
+
+assert.sameValue(
+  dt2.toString({ calendarName: "auto" }),
+  "1976-11-18T15:23:00[u-ca=bogus]",
+  "Don't show calendar if calendarName = auto & PlainDateTime has non-ISO calendar"
+);
diff --git a/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-invalid-string.js b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-invalid-string.js
index 985ad225ac..e17d9d1e44 100644
--- a/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-invalid-string.js
+++ b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-invalid-string.js
@@ -15,4 +15,11 @@ features: [Temporal]
 ---*/
 
 const datetime = new Temporal.PlainDateTime(2000, 5, 2, 12, 34, 56, 987, 654, 321);
-assert.throws(RangeError, () => datetime.toString({ calendarName: "other string" }));
+const invalidCals = ["other string", "ALWAYS", "sometimes", "auto\0"];
+
+invalidCals.forEach((cal) => {
+  assert.throws(
+    RangeError,
+    () => datetime.toString({ calendarName: cal }),
+    `invalid calendar (${cal})`);
+});
diff --git a/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-never.js b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-never.js
new file mode 100644
index 0000000000..a27cec98d2
--- /dev/null
+++ b/test/built-ins/Temporal/PlainDateTime/prototype/toString/calendarname-never.js
@@ -0,0 +1,26 @@
+// Copyright (C) 2022 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.plaindatetime.prototype.tostring
+description: Do not show calendar if calendar name option is "never"
+features: [Temporal]
+---*/
+
+const dt = new Temporal.PlainDateTime(1976, 11, 18, 15, 23);
+const cal = {
+  toString() { return "bogus"; }
+};
+const expected = "1976-11-18T15:23:00";
+
+assert.sameValue(
+  dt.toString({ calendarName: "never" }),
+  expected,
+  "Do not show calendar if calendarName = never"
+);
+
+assert.sameValue(
+  dt.withCalendar(cal).toString({ calendarName: "never" }),
+  expected,
+  "Do not show calendar when calendarName = never, even if non-ISO calendar is used"
+);
diff --git a/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-always.js b/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-always.js
new file mode 100644
index 0000000000..727b24ce90
--- /dev/null
+++ b/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-always.js
@@ -0,0 +1,16 @@
+// Copyright (C) 2022 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.plaindatetime.prototype.tostring
+description: Show calendar when calendarName is "always"
+features: [Temporal]
+---*/
+
+const dt = new Temporal.PlainDateTime(1976, 11, 18, 15, 23, 0, 0, 0, 0, "gregory");
+
+assert.sameValue(
+  dt.toString({ calendarName: "always" }),
+  "1976-11-18T15:23:00[u-ca=gregory]",
+  "shows non-ISO calendar if calendarName = always"
+);
diff --git a/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-auto.js b/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-auto.js
new file mode 100644
index 0000000000..2f9586a83d
--- /dev/null
+++ b/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-auto.js
@@ -0,0 +1,14 @@
+// Copyright (C) 2022 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.plaindatetime.prototype.tostring
+description: Possibly display calendar when calendarName is "auto"
+features: [Temporal]
+---*/
+
+const dt = new Temporal.PlainDateTime(1976, 11, 18, 15, 23, 0, 0, 0, 0, "gregory");
+const expected = "1976-11-18T15:23:00[u-ca=gregory]";
+
+assert.sameValue(dt.toString(), expected, "shows non-ISO calendar by default (no arguments)");
+assert.sameValue(dt.toString({ calendarName: "auto" }), expected, "shows only non-ISO calendar if calendarName = auto");
diff --git a/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-never.js b/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-never.js
new file mode 100644
index 0000000000..1bd9018a21
--- /dev/null
+++ b/test/intl402/Temporal/PlainDateTime/prototype/toString/calendarname-never.js
@@ -0,0 +1,16 @@
+// Copyright (C) 2022 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.plaindatetime.prototype.tostring
+description: Do not show calendar (even non-ISO calendars) if calendarName = "never"
+features: [Temporal]
+---*/
+
+const dt = new Temporal.PlainDateTime(1976, 11, 18, 15, 23);
+
+assert.sameValue(
+  dt.withCalendar("gregory").toString({ calendarName: "never" }),
+  "1976-11-18T15:23:00",
+  "omits non-ISO calendar if calendarName = never"
+);