diff --git a/changelog/7040.breaking.rst b/changelog/7040.breaking.rst
new file mode 100644
index 000000000..897b2c0a9
--- /dev/null
+++ b/changelog/7040.breaking.rst
@@ -0,0 +1,6 @@
+``-k`` no longer matches against the names of the directories outside the test session root.
+
+Also, ``pytest.Package.name`` is now just the name of the directory containing the package's
+``__init__.py`` file, instead of the full path. This is consistent with how the other nodes
+are named, and also one of the reasons why ``-k`` would match against any directory containing
+the test suite.
diff --git a/src/_pytest/mark/__init__.py b/src/_pytest/mark/__init__.py
index 242b1e0ca..1cd6e74c9 100644
--- a/src/_pytest/mark/__init__.py
+++ b/src/_pytest/mark/__init__.py
@@ -136,7 +136,7 @@ class KeywordMatcher:
         import pytest
 
         for item in item.listchain():
-            if not isinstance(item, pytest.Instance):
+            if not isinstance(item, (pytest.Instance, pytest.Session)):
                 mapped_names.add(item.name)
 
         # Add the names added as extra keywords to current or parent items
diff --git a/src/_pytest/python.py b/src/_pytest/python.py
index 0613e6eda..76fccb4a1 100644
--- a/src/_pytest/python.py
+++ b/src/_pytest/python.py
@@ -571,8 +571,7 @@ class Package(Module):
         nodes.FSCollector.__init__(
             self, fspath, parent=parent, config=config, session=session, nodeid=nodeid
         )
-
-        self.name = fspath.dirname
+        self.name = os.path.basename(str(fspath.dirname))
 
     def setup(self):
         # not using fixtures to call setup_module here because autouse fixtures
diff --git a/testing/test_collection.py b/testing/test_collection.py
index 2fd832dc6..dfbfe9ba8 100644
--- a/testing/test_collection.py
+++ b/testing/test_collection.py
@@ -1004,7 +1004,7 @@ def test_collect_init_tests(testdir):
     result.stdout.fnmatch_lines(
         [
             "collected 2 items",
-            "<Package *",
+            "<Package tests>",
             "  <Module __init__.py>",
             "    <Function test_init>",
             "  <Module test_foo.py>",
@@ -1015,7 +1015,7 @@ def test_collect_init_tests(testdir):
     result.stdout.fnmatch_lines(
         [
             "collected 2 items",
-            "<Package *",
+            "<Package tests>",
             "  <Module __init__.py>",
             "    <Function test_init>",
             "  <Module test_foo.py>",
@@ -1027,7 +1027,7 @@ def test_collect_init_tests(testdir):
     result.stdout.fnmatch_lines(
         [
             "collected 2 items",
-            "<Package */tests>",
+            "<Package tests>",
             "  <Module __init__.py>",
             "    <Function test_init>",
             "  <Module test_foo.py>",
@@ -1039,7 +1039,7 @@ def test_collect_init_tests(testdir):
     result.stdout.fnmatch_lines(
         [
             "collected 2 items",
-            "<Package */tests>",
+            "<Package tests>",
             "  <Module __init__.py>",
             "    <Function test_init>",
             "  <Module test_foo.py>",
@@ -1048,12 +1048,12 @@ def test_collect_init_tests(testdir):
     )
     result = testdir.runpytest("./tests/test_foo.py", "--collect-only")
     result.stdout.fnmatch_lines(
-        ["<Package */tests>", "  <Module test_foo.py>", "    <Function test_foo>"]
+        ["<Package tests>", "  <Module test_foo.py>", "    <Function test_foo>"]
     )
     result.stdout.no_fnmatch_line("*test_init*")
     result = testdir.runpytest("./tests/__init__.py", "--collect-only")
     result.stdout.fnmatch_lines(
-        ["<Package */tests>", "  <Module __init__.py>", "    <Function test_init>"]
+        ["<Package tests>", "  <Module __init__.py>", "    <Function test_init>"]
     )
     result.stdout.no_fnmatch_line("*test_foo*")
 
diff --git a/testing/test_mark.py b/testing/test_mark.py
index 1c983b5af..c14f770da 100644
--- a/testing/test_mark.py
+++ b/testing/test_mark.py
@@ -834,6 +834,36 @@ class TestKeywordSelection:
         deselected_tests = dlist[0].items
         assert len(deselected_tests) == 1
 
+    def test_no_match_directories_outside_the_suite(self, testdir):
+        """
+        -k should not match against directories containing the test suite (#7040).
+        """
+        test_contents = """
+            def test_aaa(): pass
+            def test_ddd(): pass
+        """
+        testdir.makepyfile(
+            **{"ddd/tests/__init__.py": "", "ddd/tests/test_foo.py": test_contents}
+        )
+
+        def get_collected_names(*args):
+            _, rec = testdir.inline_genitems(*args)
+            calls = rec.getcalls("pytest_collection_finish")
+            assert len(calls) == 1
+            return [x.name for x in calls[0].session.items]
+
+        # sanity check: collect both tests in normal runs
+        assert get_collected_names() == ["test_aaa", "test_ddd"]
+
+        # do not collect anything based on names outside the collection tree
+        assert get_collected_names("-k", testdir.tmpdir.basename) == []
+
+        # "-k ddd" should only collect "test_ddd", but not
+        # 'test_aaa' just because one of its parent directories is named "ddd";
+        # this was matched previously because Package.name would contain the full path
+        # to the package
+        assert get_collected_names("-k", "ddd") == ["test_ddd"]
+
 
 class TestMarkDecorator:
     @pytest.mark.parametrize(