diff --git a/ddtrace/_trace/tracer.py b/ddtrace/_trace/tracer.py
index 12cd4d56197..7af6711fb83 100644
--- a/ddtrace/_trace/tracer.py
+++ b/ddtrace/_trace/tracer.py
@@ -67,6 +67,23 @@
 AnyCallable = TypeVar("AnyCallable", bound=Callable)
 
 
+def _default_wrap_span_name(f: Callable) -> str:
+    qualname_parts = f.__qualname__.split(".")
+
+    # Functions defined in local scopes should not include <locals> in the name.
+    if len(qualname_parts) <= 1 or qualname_parts[-2] == "<locals>":
+        return f"{f.__module__}.{f.__name__}"
+
+    try:
+        local_scope_index = len(qualname_parts) - 1 - qualname_parts[::-1].index("<locals>")
+    except ValueError:
+        scoped_qualname = f.__qualname__
+    else:
+        scoped_qualname = ".".join(qualname_parts[local_scope_index + 1 :])
+
+    return f"{f.__module__}.{scoped_qualname}"
+
+
 def _default_span_processors_factory(
     profiling_span_processor: EndpointCallCounterProcessor,
 ) -> list[SpanProcessor]:
@@ -812,8 +829,7 @@ def execute():
         """
 
         def wrap_decorator(f: AnyCallable) -> AnyCallable:
-            # FIXME[matt] include the class name for methods.
-            span_name = name if name else "%s.%s" % (f.__module__, f.__name__)
+            span_name = name if name else _default_wrap_span_name(f)
 
             # detect if the the given function is a coroutine and/or a generator
             # to use the right decorator; this initial check ensures that the
diff --git a/releasenotes/notes/tracing-wrap-default-name-class-scope-9f2b8e3a1c5d4f67.yaml b/releasenotes/notes/tracing-wrap-default-name-class-scope-9f2b8e3a1c5d4f67.yaml
new file mode 100644
index 00000000000..6956c1c395f
--- /dev/null
+++ b/releasenotes/notes/tracing-wrap-default-name-class-scope-9f2b8e3a1c5d4f67.yaml
@@ -0,0 +1,5 @@
+---
+features:
+  - |
+    tracing: The default name for spans generated by the ``@wrap`` decorator now
+    includes the class name for methods.
diff --git a/tests/tracer/test_tracer.py b/tests/tracer/test_tracer.py
index 08739274ad0..85545d80e83 100644
--- a/tests/tracer/test_tracer.py
+++ b/tests/tracer/test_tracer.py
@@ -225,9 +225,20 @@ def i(cls):
         self.assertEqual(f.i(), 3)
 
         self.assert_span_count(3)
-        self.spans[0].assert_matches(name="tests.tracer.test_tracer.s")
-        self.spans[1].assert_matches(name="tests.tracer.test_tracer.c")
-        self.spans[2].assert_matches(name="tests.tracer.test_tracer.i")
+        self.spans[0].assert_matches(name="tests.tracer.test_tracer.Foo.s")
+        self.spans[1].assert_matches(name="tests.tracer.test_tracer.Foo.c")
+        self.spans[2].assert_matches(name="tests.tracer.test_tracer.Foo.i")
+
+    def test_tracer_wrap_local_function_no_locals_in_name(self):
+        @self.tracer.wrap()
+        def local_func():
+            pass
+
+        local_func()
+
+        self.assert_span_count(1)
+        self.spans[0].assert_matches(name="tests.tracer.test_tracer.local_func")
+        assert "<locals>" not in self.spans[0].name
 
     def test_tracer_wrap_factory(self):
         def wrap_executor(tracer, fn, args, kwargs, span_name=None, service=None, resource=None, span_type=None):