diff --git a/dvc/repo/run.py b/dvc/repo/run.py
index 43b17f53b9..02cbf6fafd 100644
--- a/dvc/repo/run.py
+++ b/dvc/repo/run.py
@@ -11,7 +11,9 @@
 
 
 def is_valid_name(name: str):
-    return not {"\\", "/", "@", ":"} & set(name)
+    from ..stage import INVALID_STAGENAME_CHARS
+
+    return not INVALID_STAGENAME_CHARS & set(name)
 
 
 def _get_file_path(kwargs):
diff --git a/dvc/stage/__init__.py b/dvc/stage/__init__.py
index a1101f0715..aef2c81171 100644
--- a/dvc/stage/__init__.py
+++ b/dvc/stage/__init__.py
@@ -2,6 +2,7 @@
 import os
 import pathlib
 import signal
+import string
 import subprocess
 import threading
 from itertools import chain, product
@@ -29,6 +30,8 @@
 from .params import OutputParams
 
 logger = logging.getLogger(__name__)
+# Disallow all punctuation characters except hyphen and underscore
+INVALID_STAGENAME_CHARS = set(string.punctuation) - {"_", "-"}
 
 
 def loads_from(cls, repo, path, wdir, data):
diff --git a/dvc/stage/exceptions.py b/dvc/stage/exceptions.py
index 19d07aea67..a98ef154a9 100644
--- a/dvc/stage/exceptions.py
+++ b/dvc/stage/exceptions.py
@@ -113,7 +113,4 @@ def __init__(self, name, file):
 
 class InvalidStageName(DvcException):
     def __init__(self,):
-        super().__init__(
-            "Stage name cannot contain invalid characters: "
-            "'\\', '/', '@' and ':'."
-        )
+        super().__init__("Stage name cannot contain punctuation characters.")
diff --git a/tests/func/test_repro.py b/tests/func/test_repro.py
index 10652b14d1..7c6cfcb143 100644
--- a/tests/func/test_repro.py
+++ b/tests/func/test_repro.py
@@ -94,14 +94,14 @@ def test(self):
             deps=[self.FOO],
             outs=["bar.txt"],
             cmd="echo bar > bar.txt",
-            name="copybarbar.txt",
+            name="copybarbar-txt",
         )
 
         self._run(
             deps=["bar.txt"],
             outs=["baz.txt"],
             cmd="echo baz > baz.txt",
-            name="copybazbaz.txt",
+            name="copybazbaz-txt",
         )
 
         stage_dump = {
@@ -657,7 +657,7 @@ def test(self):
 class TestReproPhony(TestReproChangedData):
     def test(self):
         stage = self._run(
-            cmd="cat " + self.file1, deps=[self.file1], name="no_cmd?"
+            cmd="cat " + self.file1, deps=[self.file1], name="no_cmd"
         )
 
         self.swap_foo_with_bar()
diff --git a/tests/func/test_run_multistage.py b/tests/func/test_run_multistage.py
index a84a38620d..bb8e7d489b 100644
--- a/tests/func/test_run_multistage.py
+++ b/tests/func/test_run_multistage.py
@@ -160,10 +160,17 @@ def test_run_dump_on_multistage(tmp_dir, dvc):
     }
 
 
-def test_run_with_invalid_stage_name(tmp_dir, dvc, run_copy):
-    tmp_dir.dvc_gen("foo", "foo")
+@pytest.mark.parametrize(
+    "char", ["@:", "#", "$", ":", "/", "\\", ".", ";", ","]
+)
+def test_run_with_invalid_stage_name(run_copy, char):
     with pytest.raises(InvalidStageName):
-        run_copy("foo", "bar", name="email@https://dvc.org")
+        run_copy("foo", "bar", name="copy_name-{}".format(char))
+
+
+def test_run_with_name_having_hyphen_underscore(tmp_dir, dvc, run_copy):
+    tmp_dir.dvc_gen("foo", "foo")
+    run_copy("foo", "bar", name="copy-foo_bar")
 
 
 def test_run_already_exists(tmp_dir, dvc, run_copy):