diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index 1e946d325ace1..da261907565a1 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -41,6 +41,7 @@ Bug fixes
 - Bug in :meth:`Series.dt.isocalendar` and :meth:`DatetimeIndex.isocalendar` that returned incorrect year for certain dates (:issue:`36032`)
 - Bug in :class:`DataFrame` indexing returning an incorrect :class:`Series` in some cases when the series has been altered and a cache not invalidated (:issue:`33675`)
 - Bug in :meth:`DataFrame.corr` causing subsequent indexing lookups to be incorrect (:issue:`35882`)
+- Bug in :meth:`import_optional_dependency` returning incorrect package names in cases where package name is different from import name (:issue:`35948`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/compat/_optional.py b/pandas/compat/_optional.py
index 689c7c889ef66..40688a3978cfc 100644
--- a/pandas/compat/_optional.py
+++ b/pandas/compat/_optional.py
@@ -33,6 +33,19 @@
     "numba": "0.46.0",
 }
 
+# A mapping from import name to package name (on PyPI) for packages where
+# these two names are different.
+
+INSTALL_MAPPING = {
+    "bs4": "beautifulsoup4",
+    "bottleneck": "Bottleneck",
+    "lxml.etree": "lxml",
+    "odf": "odfpy",
+    "pandas_gbq": "pandas-gbq",
+    "sqlalchemy": "SQLAlchemy",
+    "jinja2": "Jinja2",
+}
+
 
 def _get_version(module: types.ModuleType) -> str:
     version = getattr(module, "__version__", None)
@@ -82,9 +95,13 @@ def import_optional_dependency(
         is False, or when the package's version is too old and `on_version`
         is ``'warn'``.
     """
+
+    package_name = INSTALL_MAPPING.get(name)
+    install_name = package_name if package_name is not None else name
+
     msg = (
-        f"Missing optional dependency '{name}'. {extra} "
-        f"Use pip or conda to install {name}."
+        f"Missing optional dependency '{install_name}'. {extra} "
+        f"Use pip or conda to install {install_name}."
     )
     try:
         module = importlib.import_module(name)