diff --git a/Lib/pathlib.py b/Lib/pathlib.py
index d3d1af8..c1ec07a 100644
--- a/Lib/pathlib.py
+++ b/Lib/pathlib.py
@@ -749,6 +749,10 @@
         """Return a new path with the file name changed."""
         if not self.name:
             raise ValueError("%r has an empty name" % (self,))
+        drv, root, parts = self._flavour.parse_parts((name,))
+        if (not name or name[-1] in [self._flavour.sep, self._flavour.altsep]
+            or drv or root or len(parts) != 1):
+            raise ValueError("Invalid name %r" % (name))
         return self._from_parsed_parts(self._drv, self._root,
                                        self._parts[:-1] + [name])
 
diff --git a/Lib/test/test_pathlib.py b/Lib/test/test_pathlib.py
index 6378d8c..2c3fce7 100644
--- a/Lib/test/test_pathlib.py
+++ b/Lib/test/test_pathlib.py
@@ -540,6 +540,10 @@
         self.assertRaises(ValueError, P('').with_name, 'd.xml')
         self.assertRaises(ValueError, P('.').with_name, 'd.xml')
         self.assertRaises(ValueError, P('/').with_name, 'd.xml')
+        self.assertRaises(ValueError, P('a/b').with_name, '')
+        self.assertRaises(ValueError, P('a/b').with_name, '/c')
+        self.assertRaises(ValueError, P('a/b').with_name, 'c/')
+        self.assertRaises(ValueError, P('a/b').with_name, 'c/d')
 
     def test_with_suffix_common(self):
         P = self.cls
@@ -950,6 +954,10 @@
         self.assertRaises(ValueError, P('c:').with_name, 'd.xml')
         self.assertRaises(ValueError, P('c:/').with_name, 'd.xml')
         self.assertRaises(ValueError, P('//My/Share').with_name, 'd.xml')
+        self.assertRaises(ValueError, P('c:a/b').with_name, 'd:')
+        self.assertRaises(ValueError, P('c:a/b').with_name, 'd:e')
+        self.assertRaises(ValueError, P('c:a/b').with_name, 'd:/e')
+        self.assertRaises(ValueError, P('c:a/b').with_name, '//My/Share')
 
     def test_with_suffix(self):
         P = self.cls