diff --git a/Cabal/src/Distribution/PackageDescription/Check.hs b/Cabal/src/Distribution/PackageDescription/Check.hs
index f743b62365d..ee50418e928 100644
--- a/Cabal/src/Distribution/PackageDescription/Check.hs
+++ b/Cabal/src/Distribution/PackageDescription/Check.hs
@@ -413,9 +413,13 @@ checkPackageDescription
     checkPackageId package_
     -- TODO `name` is caught at parse level, remove this test.
     let pn = packageName package_
+        pns = unPackageName pn
     checkP
-      (null . unPackageName $ pn)
+      (null pns)
       (PackageBuildImpossible NoNameField)
+    checkP
+      (any (not . isAscii) pns)
+      (PackageDistInexcusable NonASCIIName)
     -- TODO `version` is caught at parse level, remove this test.
     checkP
       (nullVersion == packageVersion package_)
diff --git a/Cabal/src/Distribution/PackageDescription/Check/Warning.hs b/Cabal/src/Distribution/PackageDescription/Check/Warning.hs
index 3ff5430eac7..6d474fab477 100644
--- a/Cabal/src/Distribution/PackageDescription/Check/Warning.hs
+++ b/Cabal/src/Distribution/PackageDescription/Check/Warning.hs
@@ -142,6 +142,7 @@ filterPackageChecksByIdString cs ss =
 data CheckExplanation
   = ParseWarning FilePath PWarning
   | NoNameField
+  | NonASCIIName
   | NoVersionField
   | NoTarget
   | UnnamedInternal
@@ -309,6 +310,7 @@ extractCheckExplanation (PackageDistInexcusable e) = e
 data CheckExplanationID
   = CIParseWarning
   | CINoNameField
+  | CINonASCIIName
   | CINoVersionField
   | CINoTarget
   | CIUnnamedInternal
@@ -455,6 +457,7 @@ data CheckExplanationID
 checkExplanationId :: CheckExplanation -> CheckExplanationID
 checkExplanationId (ParseWarning{}) = CIParseWarning
 checkExplanationId (NoNameField{}) = CINoNameField
+checkExplanationId (NonASCIIName{}) = CINonASCIIName
 checkExplanationId (NoVersionField{}) = CINoVersionField
 checkExplanationId (NoTarget{}) = CINoTarget
 checkExplanationId (UnnamedInternal{}) = CIUnnamedInternal
@@ -608,6 +611,7 @@ ppCheckExplanationId :: CheckExplanationID -> CheckExplanationIDString
 --   $ cabal run Cabal-tests:unit-tests -- --pattern=Parsimonious
 ppCheckExplanationId CIParseWarning = "parser-warning"
 ppCheckExplanationId CINoNameField = "no-name-field"
+ppCheckExplanationId CINonASCIIName = "non-ascii-name"
 ppCheckExplanationId CINoVersionField = "no-version-field"
 ppCheckExplanationId CINoTarget = "no-target"
 ppCheckExplanationId CIUnnamedInternal = "unnamed-internal-library"
@@ -795,6 +799,7 @@ ppWarnLang LangCPlusPlus = "C++"
 ppExplanation :: CheckExplanation -> String
 ppExplanation (ParseWarning fp pp) = showPWarning fp pp
 ppExplanation NoNameField = "No 'name' field."
+ppExplanation NonASCIIName = "Non-ASCII characters in 'name' field."
 ppExplanation NoVersionField = "No 'version' field."
 ppExplanation NoTarget =
   "No executables, libraries, tests, or benchmarks found. Nothing to do."
diff --git a/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/cabal.out b/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/cabal.out
new file mode 100644
index 00000000000..6064676ea62
--- /dev/null
+++ b/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/cabal.out
@@ -0,0 +1,5 @@
+# cabal check
+The following errors will cause portability problems on other environments:
+Error: [name-no-match] The filename './pkg.cabal' does not match package name (expected: 'pkg-?.cabal')
+Error: [non-ascii-name] Non-ASCII characters in 'name' field.
+Error: Hackage would reject this package.
diff --git a/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/cabal.test.hs b/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/cabal.test.hs
new file mode 100644
index 00000000000..5d037e67116
--- /dev/null
+++ b/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/cabal.test.hs
@@ -0,0 +1,5 @@
+import Test.Cabal.Prelude
+
+-- Non ASCII charaters in package name.
+main = cabalTest $
+  fails $ cabal "check" []
diff --git a/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/pkg.cabal b/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/pkg.cabal
new file mode 100644
index 00000000000..71532e30e51
--- /dev/null
+++ b/cabal-testsuite/PackageTests/Check/ConfiguredPackage/Fields/NonASCIIName/pkg.cabal
@@ -0,0 +1,16 @@
+cabal-version: 3.0
+name: pkg-α
+  -- Cabal testsuite sadly chokes when copying files with
+  -- non-ASCII characters in them. So for this test, in
+  -- the output file, you will get an error for filename/
+  -- name mismatch, too.
+description: description
+synopsis: synopsis
+version: 0
+category: example
+maintainer: none@example.com
+license: GPL-3.0-or-later
+
+library
+  exposed-modules: Module
+  default-language: Haskell2010
diff --git a/changelog.d/pr-11198 b/changelog.d/pr-11198
new file mode 100644
index 00000000000..7b534e22e37
--- /dev/null
+++ b/changelog.d/pr-11198
@@ -0,0 +1,9 @@
+---
+synopsis: Warn on non-ASCII characters in `name`
+packages: [Cabal, cabal-install]
+prs: 11198
+issues: 11197
+---
+
+`cabal check` now warns about packages with non-ASCII characters
+in their name (they are not accepted by Hackage).
diff --git a/doc/cabal-commands.rst b/doc/cabal-commands.rst
index b9354db992d..23adbeef1b4 100644
--- a/doc/cabal-commands.rst
+++ b/doc/cabal-commands.rst
@@ -1385,6 +1385,7 @@ A list of all warnings with their constructor:
 
 - ``parser-warning``: inherited from parser.
 - ``no-name-field``: missing ``name`` field.
+- ``non-ascii-name``: non-ASCII characters in ``name`` field.
 - ``no-version-field``: missing ``version`` field.
 - ``no-target``: missing target in ``.cabal``.
 - ``unnamed-internal-library``: unnamed internal library.