diff --git a/mypy/checker.py b/mypy/checker.py
index b8b85be3fbe8..957da2cd33bc 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -5295,10 +5295,15 @@ def format_expr_type() -> str:
             else:
                 return f"Expression has type {typ}"
 
+        def get_expr_name() -> str:
+            if isinstance(expr, (NameExpr, MemberExpr)):
+                return f'"{expr.name}"'
+            else:
+                # return type if expr has no name
+                return format_type(t, self.options)
+
         if isinstance(t, FunctionLike):
-            self.fail(
-                message_registry.FUNCTION_ALWAYS_TRUE.format(format_type(t, self.options)), expr
-            )
+            self.fail(message_registry.FUNCTION_ALWAYS_TRUE.format(get_expr_name()), expr)
         elif isinstance(t, UnionType):
             self.fail(message_registry.TYPE_ALWAYS_TRUE_UNIONTYPE.format(format_expr_type()), expr)
         elif isinstance(t, Instance) and t.type.fullname == "typing.Iterable":
diff --git a/test-data/unit/check-errorcodes.test b/test-data/unit/check-errorcodes.test
index fc498c9aa6c0..2d97b3ccec90 100644
--- a/test-data/unit/check-errorcodes.test
+++ b/test-data/unit/check-errorcodes.test
@@ -900,11 +900,11 @@ if any_or_object:
 # flags: --strict-optional
 def f():
     pass
-if f:  # E: Function "Callable[[], Any]" could always be true in boolean context  [truthy-function]
+if f:  # E: Function "f" could always be true in boolean context  [truthy-function]
     pass
-if not f:  # E: Function "Callable[[], Any]" could always be true in boolean context  [truthy-function]
+if not f:  # E: Function "f" could always be true in boolean context  [truthy-function]
     pass
-conditional_result = 'foo' if f else 'bar'  # E: Function "Callable[[], Any]" could always be true in boolean context  [truthy-function]
+conditional_result = 'foo' if f else 'bar'  # E: Function "f" could always be true in boolean context  [truthy-function]
 
 [case testTruthyIterable]
 # flags: --strict-optional --enable-error-code truthy-iterable
diff --git a/test-data/unit/check-flags.test b/test-data/unit/check-flags.test
index 244e728f3ab6..cd45ceb45834 100644
--- a/test-data/unit/check-flags.test
+++ b/test-data/unit/check-flags.test
@@ -2101,12 +2101,12 @@ import tests.foo
 import bar
 [file bar.py]
 def foo() -> int: ...
-if foo: ...  # E: Function "Callable[[], int]" could always be true in boolean context
+if foo: ...  # E: Function "foo" could always be true in boolean context
 42 + "no"  # type: ignore  # E: "type: ignore" comment without error code (consider "type: ignore[operator]" instead)
 [file tests/__init__.py]
 [file tests/foo.py]
 def foo() -> int: ...
-if foo: ...  # E: Function "Callable[[], int]" could always be true in boolean context
+if foo: ...  # E: Function "foo" could always be true in boolean context
 42 + "no"  # type: ignore
 [file mypy.ini]
 \[mypy]
diff --git a/test-data/unit/check-inline-config.test b/test-data/unit/check-inline-config.test
index db04536dd4f9..0cc2bd71270a 100644
--- a/test-data/unit/check-inline-config.test
+++ b/test-data/unit/check-inline-config.test
@@ -192,7 +192,7 @@ if foo: ...
 # mypy: enable-error-code="ignore-without-code"
 
 def foo() -> int: ...
-if foo: ...  # E: Function "Callable[[], int]" could always be true in boolean context
+if foo: ...  # E: Function "foo" could always be true in boolean context
 42 + "no"  # type: ignore  # E: "type: ignore" comment without error code (consider "type: ignore[operator]" instead)
 
 [file tests/baz.py]
diff --git a/test-data/unit/check-python38.test b/test-data/unit/check-python38.test
index 5b077c45580a..423daaf5ae8f 100644
--- a/test-data/unit/check-python38.test
+++ b/test-data/unit/check-python38.test
@@ -310,7 +310,8 @@ def f(x: int = (c := 4)) -> int:
         z2: NT  # E: Variable "NT" is not valid as a type \
                 # N: See https://mypy.readthedocs.io/en/stable/common_issues.html#variables-vs-type-aliases
 
-    if Alias := int:  # E: Function "Type[int]" could always be true in boolean context
+    if Alias := int:  # E: Function "Alias" could always be true in boolean context \
+                      # E: Function "int" could always be true in boolean context
         z3: Alias  # E: Variable "Alias" is not valid as a type \
                    # N: See https://mypy.readthedocs.io/en/stable/common_issues.html#variables-vs-type-aliases
 
diff --git a/test-data/unit/check-unreachable-code.test b/test-data/unit/check-unreachable-code.test
index a9e025632e24..b2fd44043435 100644
--- a/test-data/unit/check-unreachable-code.test
+++ b/test-data/unit/check-unreachable-code.test
@@ -936,7 +936,7 @@ class Case1:
         return False and self.missing()  # E: Right operand of "and" is never evaluated
 
     def test2(self) -> bool:
-        return not self.property_decorator_missing and self.missing()  # E: Function "Callable[[], bool]" could always be true in boolean context \
+        return not self.property_decorator_missing and self.missing()  # E: Function "property_decorator_missing" could always be true in boolean context \
             # E: Right operand of "and" is never evaluated
 
     def property_decorator_missing(self) -> bool: