diff --git a/basepath.go b/basepath.go
index 47438dd..aa1e38c 100644
--- a/basepath.go
+++ b/basepath.go
@@ -37,7 +37,16 @@ type BasePathFile struct {
 
 func (f *BasePathFile) Name() string {
 	sourcename := f.File.Name()
-	return strings.TrimPrefix(sourcename, filepath.Clean(f.path))
+	base := filepath.Clean(f.path)
+	name := strings.TrimPrefix(sourcename, base)
+	if name == sourcename {
+		// filepath.Clean drops the leading separator from the base path, so a
+		// name produced by a wrapped (nested) BasePathFile can still carry the
+		// base preceded by a separator. Strip that form as well, otherwise the
+		// base segment leaks into the reported name.
+		name = strings.TrimPrefix(sourcename, string(filepath.Separator)+base)
+	}
+	return name
 }
 
 func (f *BasePathFile) ReadDir(n int) ([]fs.DirEntry, error) {
diff --git a/basepath_test.go b/basepath_test.go
index 2ecc440..603b48e 100644
--- a/basepath_test.go
+++ b/basepath_test.go
@@ -307,3 +307,31 @@ func TestBasePathTempFile(t *testing.T) {
 		t.Fatalf("TempFile realpath leaked: expected %s, got %s", expected, actual)
 	}
 }
+
+// Regression test for #428: a nested BasePathFs must strip its own base
+// segment from BasePathFile.Name(), even though filepath.Clean drops the
+// leading separator that the wrapped (inner) file name carries.
+func TestNestedBasePathFileName(t *testing.T) {
+	baseFs := &MemMapFs{}
+	if err := baseFs.MkdirAll("/files/123", 0o777); err != nil {
+		t.Fatal(err)
+	}
+	fs1 := NewBasePathFs(baseFs, "/files")
+	fs2 := NewBasePathFs(fs1, "123")
+
+	f, err := fs2.OpenFile("/afero-test.txt", os.O_CREATE|os.O_RDWR, 0o644)
+	if err != nil {
+		t.Fatalf("open through nested BasePathFs failed: %v", err)
+	}
+	defer f.Close()
+
+	if expected, actual := "/afero-test.txt", f.Name(); expected != actual {
+		t.Fatalf("nested BasePathFile.Name() = %q, want %q", actual, expected)
+	}
+
+	// The returned name must round-trip: using it via fs2 resolves back to
+	// the same file instead of double-prepending the base segment.
+	if err := fs2.Chmod(f.Name(), 0o600); err != nil {
+		t.Fatalf("chmod via returned name failed: %v", err)
+	}
+}