diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 5b51bc9debb33..a6a5f142faf1c 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -62,8 +62,6 @@
     is_list_like,
 )
 
-from pandas.util import capitalize_first_letter
-
 if not pa_version_under10p1:
     import pyarrow as pa
 
@@ -1087,7 +1085,7 @@ def na_value(self) -> NaTType:
 
     def __eq__(self, other: object) -> bool:
         if isinstance(other, str):
-            return other in [self.name, capitalize_first_letter(self.name)]
+            return other[:1].lower() + other[1:] == self.name
 
         return super().__eq__(other)
 
diff --git a/pandas/util/__init__.py b/pandas/util/__init__.py
index 59ab324ba38ca..da109a514433f 100644
--- a/pandas/util/__init__.py
+++ b/pandas/util/__init__.py
@@ -27,7 +27,3 @@ def __getattr__(key: str):
 
 def __dir__():
     return list(globals().keys()) + ["hash_array", "hash_pandas_object"]
-
-
-def capitalize_first_letter(s: str) -> str:
-    return s[:1].upper() + s[1:]