diff --git a/CHANGELOG.md b/CHANGELOG.md
index a22e15b1c..b0f0c336a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@ Find out more about isort's release policy [here](https://pycqa.github.io/isort/
   - Fixed #1772: skip-gitignore will check files not in the git repository.
   - Fixed #1762: in some cases when skip-gitignore is set, isort fails to skip any files.
   - Fixed #1767: Encoding issues surfacing when invalid characters set in `__init__.py` files during placement.
+  - Fixed #1771: Improved handling of skips against named streamed in content.
 
 ### 5.9.1 June 21st 2021 [hotfix]
   - Fixed #1758: projects with many files and skip_ignore set can lead to a command-line overload.
diff --git a/isort/main.py b/isort/main.py
index 0c3950bc9..34ce3fdd0 100644
--- a/isort/main.py
+++ b/isort/main.py
@@ -1087,9 +1087,10 @@ def main(argv: Optional[Sequence[str]] = None, stdin: Optional[TextIOWrapper] =
         if show_files:
             sys.exit("Error: can't show files for streaming input.")
 
+        input_stream = sys.stdin if stdin is None else stdin
         if check:
             incorrectly_sorted = not api.check_stream(
-                input_stream=sys.stdin if stdin is None else stdin,
+                input_stream=input_stream,
                 config=config,
                 show_diff=show_diff,
                 file_path=file_path,
@@ -1098,15 +1099,18 @@ def main(argv: Optional[Sequence[str]] = None, stdin: Optional[TextIOWrapper] =
 
             wrong_sorted_files = incorrectly_sorted
         else:
-            api.sort_stream(
-                input_stream=sys.stdin if stdin is None else stdin,
-                output_stream=sys.stdout,
-                config=config,
-                show_diff=show_diff,
-                file_path=file_path,
-                extension=ext_format,
-                raise_on_skip=False,
-            )
+            try:
+                api.sort_stream(
+                    input_stream=input_stream,
+                    output_stream=sys.stdout,
+                    config=config,
+                    show_diff=show_diff,
+                    file_path=file_path,
+                    extension=ext_format,
+                    raise_on_skip=False,
+                )
+            except FileSkipped:
+                sys.stdout.write(input_stream.read())
     elif "/" in file_names and not allow_root:
         printer = create_terminal_printer(
             color=config.color_output, error=config.format_error, success=config.format_success
diff --git a/tests/unit/test_main.py b/tests/unit/test_main.py
index 9039787cc..78d1e9374 100644
--- a/tests/unit/test_main.py
+++ b/tests/unit/test_main.py
@@ -370,6 +370,23 @@ def build_input_content():
 import b
 
 
+def function():
+    pass
+"""
+    )
+
+    # if file is skipped it should output unchanged.
+    main.main(
+        ["-", "--filename", "x.py", "--skip", "x.py", "--filter-files"],
+        stdin=build_input_content(),
+    )
+    out, error = capsys.readouterr()
+    assert not error
+    assert out == (
+        """
+import b
+import a
+
 def function():
     pass
 """