diff --git a/src/joserfc/_rfc7519/claims.py b/src/joserfc/_rfc7519/claims.py
index 7348972..a522ab4 100644
--- a/src/joserfc/_rfc7519/claims.py
+++ b/src/joserfc/_rfc7519/claims.py
@@ -127,7 +127,7 @@ def validate_iss(self, value: str) -> None:
         value.  Use of this claim is OPTIONAL.
         """
         if not isinstance(value, str):
-            raise InvalidClaimError("str", "Claim 'str' must be a StringOrURI value")
+            raise InvalidClaimError("iss", "Claim 'iss' must be a StringOrURI value")
         self.check_value("iss", value)
 
     def validate_sub(self, value: str) -> None:
diff --git a/tests/jwt/test_claims.py b/tests/jwt/test_claims.py
index 4fc5326..065c0cb 100644
--- a/tests/jwt/test_claims.py
+++ b/tests/jwt/test_claims.py
@@ -51,11 +51,15 @@ def test_essential_claims(self):
     def test_claim_iss(self):
         claims_requests = jwt.JWTClaimsRegistry(iss={"essential": True})
         claims_requests.validate({"iss": "a"})
-        self.assertRaises(InvalidClaimError, claims_requests.validate, {"iss": 1})
         self.assertRaises(InvalidClaimError, claims_requests.validate, {"iss": True})
         self.assertRaises(InvalidClaimError, claims_requests.validate, {"iss": ["a"]})
         self.assertRaises(InvalidClaimError, claims_requests.validate, {"iss": {"a": "b"}})
 
+        with self.assertRaises(InvalidClaimError) as cm:
+            claims_requests.validate({"iss": 1})
+        self.assertEqual(cm.exception.claim, "iss")
+        self.assertIn("'iss'", cm.exception.description)
+
     def test_claim_sub(self):
         claims_requests = jwt.JWTClaimsRegistry(sub={"essential": True})
         claims_requests.validate({"sub": "a"})