Fix Creating Cultures with Sort Names

src/libraries/System.Globalization/tests/CultureInfo/CultureInfoCtor.cs

@@ -439,5 +439,14 @@ public void TestCreationWithTemporaryLCID(int lcid)
 
             Assert.NotEqual(lcid, new CultureInfo(lcid).LCID);
         }
+
+        [InlineData("zh-TW-u-co-zhuyin")]
+        [InlineData("de-DE-u-co-phoneb")]
+        [InlineData("de-u-co-phonebk")]
+        [ConditionalTheory(typeof(PlatformDetection), nameof(PlatformDetection.IsIcuGlobalization))]
+        public void TestCreationWithMangledSortName(string cultureName)
+        {
+            Assert.True(CultureInfo.GetCultureInfo(cultureName).CompareInfo.Name.Equals(cultureName, StringComparison.OrdinalIgnoreCase));
+        }
     }
 }

src/libraries/System.Private.CoreLib/src/System/Globalization/CompareInfo.Icu.cs

@@ -14,7 +14,7 @@ public partial class CompareInfo
         [NonSerialized]
         private bool _isAsciiEqualityOrdinal;
 
-        private void IcuInitSortHandle()
+        private void IcuInitSortHandle(string interopCultureName)
         {
             if (GlobalizationMode.Invariant)
             {
@@ -23,6 +23,7 @@ private void IcuInitSortHandle()
             else
             {
                 Debug.Assert(!GlobalizationMode.UseNls);
+                Debug.Assert(interopCultureName != null);
 
                 // Inline the following condition to avoid potential implementation cycles within globalization
                 //
@@ -31,7 +32,7 @@ private void IcuInitSortHandle()
                 _isAsciiEqualityOrdinal = _sortName.Length == 0 ||
                     (_sortName.Length >= 2 && _sortName[0] == 'e' && _sortName[1] == 'n' && (_sortName.Length == 2 || _sortName[2] == '-'));
 
-                _sortHandle = SortHandleCache.GetCachedSortHandle(_sortName);
+                _sortHandle = SortHandleCache.GetCachedSortHandle(interopCultureName);
             }
         }
 

src/libraries/System.Private.CoreLib/src/System/Globalization/CompareInfo.cs

@@ -191,7 +191,7 @@ private void InitSort(CultureInfo culture)
             }
             else
             {
-                IcuInitSortHandle();
+                IcuInitSortHandle(culture.InteropName!);
             }
         }
 

src/libraries/System.Private.CoreLib/src/System/Globalization/CultureData.Icu.cs

@@ -50,7 +50,11 @@ private bool InitIcuCultureDataCore()
             index = _sWindowsName.IndexOf(ICU_COLLATION_KEYWORD, StringComparison.Ordinal);
             if (index >= 0)
             {
-                _sName = string.Concat(_sWindowsName.AsSpan(0, index), "_", alternateSortName);
+                // It is possible alternateSortName not set even if the normalized culture name has "@collation=".
+                // "zh-TW-u-co-zhuyin" is a good example of that. The term "u-co-" in the name means the following part will be the sort name.
+                // That is mean "zh-TW-u-co-zhuyin" will have the equivalent ICU name "zh-TW@collation=zhuyin".
+                // In this case, we'll not change the original culture name.
+                _sName = alternateSortName.Length == 0 ? realNameBuffer : string.Concat(_sWindowsName.AsSpan(0, index), "_", alternateSortName);
             }
             else
             {

src/libraries/System.Private.CoreLib/src/System/Globalization/CultureData.cs

@@ -413,6 +413,8 @@ internal sealed partial class CultureData
         private static volatile Dictionary<string, CultureData>? s_cachedRegions;
         private static volatile Dictionary<string, string>? s_regionNames;
 
+        internal string? InteropName => _sWindowsName;
+
         internal static CultureData? GetCultureDataForRegion(string? cultureName, bool useUserOverride)
         {
             // First do a shortcut for Invariant

src/libraries/System.Private.CoreLib/src/System/Globalization/CultureInfo.cs

@@ -580,6 +580,8 @@ public static CultureInfo[] GetCultures(CultureTypes types)
         /// </summary>
         internal string SortName => _sortName ??= _cultureData.SortName;
 
+        internal string? InteropName => _cultureData.InteropName;
+
         public string IetfLanguageTag =>
                 // special case the compatibility cultures
                 Name switch