diff --git a/homeassistant/util/unit_system.py b/homeassistant/util/unit_system.py
index 194b8d82dbb..fcb8c0a4f16 100644
--- a/homeassistant/util/unit_system.py
+++ b/homeassistant/util/unit_system.py
@@ -23,7 +23,6 @@ from homeassistant.const import (
     UnitOfTemperature,
     UnitOfVolume,
 )
-from homeassistant.helpers.frame import report
 
 from .unit_conversion import (
     DistanceConverter,
@@ -121,35 +120,6 @@ class UnitSystem:
         self.wind_speed_unit = wind_speed
         self._conversions = conversions
 
-    @property
-    def name(self) -> str:
-        """Return the name of the unit system."""
-        report(
-            (
-                "accesses the `name` property of the unit system. "
-                "This is deprecated and will stop working in Home Assistant 2023.1. "
-                "Please adjust to use instance check instead."
-            ),
-            error_if_core=False,
-        )
-        if self is IMPERIAL_SYSTEM:
-            # kept for compatibility reasons, with associated warning above
-            return _CONF_UNIT_SYSTEM_IMPERIAL
-        return self._name
-
-    @property
-    def is_metric(self) -> bool:
-        """Determine if this is the metric unit system."""
-        report(
-            (
-                "accesses the `is_metric` property of the unit system. "
-                "This is deprecated and will stop working in Home Assistant 2023.1. "
-                "Please adjust to use instance check instead."
-            ),
-            error_if_core=False,
-        )
-        return self is METRIC_SYSTEM
-
     def temperature(self, temperature: float, from_unit: str) -> float:
         """Convert the given temperature to this unit system."""
         if not isinstance(temperature, Number):
diff --git a/tests/components/config/test_core.py b/tests/components/config/test_core.py
index 67977c96a2b..f3283d32972 100644
--- a/tests/components/config/test_core.py
+++ b/tests/components/config/test_core.py
@@ -9,6 +9,7 @@ from homeassistant.components import config
 from homeassistant.components.websocket_api.const import TYPE_RESULT
 from homeassistant.const import CONF_UNIT_SYSTEM, CONF_UNIT_SYSTEM_IMPERIAL
 from homeassistant.util import dt as dt_util, location
+from homeassistant.util.unit_system import US_CUSTOMARY_SYSTEM
 
 
 @pytest.fixture
@@ -55,7 +56,7 @@ async def test_websocket_core_update(hass, client):
     assert hass.config.longitude != 50
     assert hass.config.elevation != 25
     assert hass.config.location_name != "Huis"
-    assert hass.config.units.name != CONF_UNIT_SYSTEM_IMPERIAL
+    assert hass.config.units is not US_CUSTOMARY_SYSTEM
     assert hass.config.time_zone != "America/New_York"
     assert hass.config.external_url != "https://www.example.com"
     assert hass.config.internal_url != "http://example.com"
@@ -91,7 +92,7 @@ async def test_websocket_core_update(hass, client):
     assert hass.config.longitude == 50
     assert hass.config.elevation == 25
     assert hass.config.location_name == "Huis"
-    assert hass.config.units.name == CONF_UNIT_SYSTEM_IMPERIAL
+    assert hass.config.units is US_CUSTOMARY_SYSTEM
     assert hass.config.external_url == "https://www.example.com"
     assert hass.config.internal_url == "http://example.local"
     assert hass.config.currency == "USD"
diff --git a/tests/test_config.py b/tests/test_config.py
index 00b0ae63c0b..1d804736c9d 100644
--- a/tests/test_config.py
+++ b/tests/test_config.py
@@ -412,7 +412,7 @@ async def test_loading_configuration_from_storage(hass, hass_storage):
     assert hass.config.longitude == 13
     assert hass.config.elevation == 10
     assert hass.config.location_name == "Home"
-    assert hass.config.units.name == CONF_UNIT_SYSTEM_METRIC
+    assert hass.config.units is METRIC_SYSTEM
     assert hass.config.time_zone == "Europe/Copenhagen"
     assert hass.config.external_url == "https://www.example.com"
     assert hass.config.internal_url == "http://example.local"
@@ -446,7 +446,7 @@ async def test_loading_configuration_from_storage_with_yaml_only(hass, hass_stor
     assert hass.config.longitude == 13
     assert hass.config.elevation == 10
     assert hass.config.location_name == "Home"
-    assert hass.config.units.name == CONF_UNIT_SYSTEM_METRIC
+    assert hass.config.units is METRIC_SYSTEM
     assert hass.config.time_zone == "Europe/Copenhagen"
     assert len(hass.config.allowlist_external_dirs) == 3
     assert "/etc" in hass.config.allowlist_external_dirs
@@ -517,7 +517,7 @@ async def test_override_stored_configuration(hass, hass_storage):
     assert hass.config.longitude == 13
     assert hass.config.elevation == 10
     assert hass.config.location_name == "Home"
-    assert hass.config.units.name == CONF_UNIT_SYSTEM_METRIC
+    assert hass.config.units is METRIC_SYSTEM
     assert hass.config.time_zone == "Europe/Copenhagen"
     assert len(hass.config.allowlist_external_dirs) == 3
     assert "/etc" in hass.config.allowlist_external_dirs
@@ -550,7 +550,7 @@ async def test_loading_configuration(hass):
     assert hass.config.longitude == 50
     assert hass.config.elevation == 25
     assert hass.config.location_name == "Huis"
-    assert hass.config.units.name == CONF_UNIT_SYSTEM_IMPERIAL
+    assert hass.config.units is US_CUSTOMARY_SYSTEM
     assert hass.config.time_zone == "America/New_York"
     assert hass.config.external_url == "https://www.example.com"
     assert hass.config.internal_url == "http://example.local"
diff --git a/tests/util/test_unit_system.py b/tests/util/test_unit_system.py
index 4813bc34a3a..0c8ce7a191b 100644
--- a/tests/util/test_unit_system.py
+++ b/tests/util/test_unit_system.py
@@ -311,51 +311,6 @@ def test_properties():
     assert METRIC_SYSTEM.accumulated_precipitation_unit == UnitOfLength.MILLIMETERS
 
 
-@pytest.mark.parametrize(
-    "unit_system, expected_flag",
-    [
-        (METRIC_SYSTEM, True),
-        (IMPERIAL_SYSTEM, False),
-    ],
-)
-def test_is_metric(
-    caplog: pytest.LogCaptureFixture, unit_system: UnitSystem, expected_flag: bool
-):
-    """Test the is metric flag."""
-    assert unit_system.is_metric == expected_flag
-    assert (
-        "Detected code that accesses the `is_metric` property of the unit system."
-        in caplog.text
-    )
-
-
-@pytest.mark.parametrize(
-    "unit_system, expected_name, expected_private_name",
-    [
-        (METRIC_SYSTEM, _CONF_UNIT_SYSTEM_METRIC, _CONF_UNIT_SYSTEM_METRIC),
-        (IMPERIAL_SYSTEM, _CONF_UNIT_SYSTEM_IMPERIAL, _CONF_UNIT_SYSTEM_US_CUSTOMARY),
-        (
-            US_CUSTOMARY_SYSTEM,
-            _CONF_UNIT_SYSTEM_IMPERIAL,
-            _CONF_UNIT_SYSTEM_US_CUSTOMARY,
-        ),
-    ],
-)
-def test_deprecated_name(
-    caplog: pytest.LogCaptureFixture,
-    unit_system: UnitSystem,
-    expected_name: str,
-    expected_private_name: str,
-) -> None:
-    """Test the name is deprecated."""
-    assert unit_system.name == expected_name
-    assert unit_system._name == expected_private_name
-    assert (
-        "Detected code that accesses the `name` property of the unit system."
-        in caplog.text
-    )
-
-
 @pytest.mark.parametrize(
     "key, expected_system",
     [