diff --git a/CORE_TEAM_GUIDE.md b/CORE_TEAM_GUIDE.md
index cf1dc152d68..9ebb045df58 100644
--- a/CORE_TEAM_GUIDE.md
+++ b/CORE_TEAM_GUIDE.md
@@ -107,7 +107,8 @@ Here’s a typical workflow for triaging a newly opened issue or discussion:
 
 6. **Is this a usage question?**
 
-   We prefer that usage questions are asked on StackOverflow with the [`python-xarray` tag](https://stackoverflow.com/questions/tagged/python-xarray).
+   We prefer that usage questions are asked on StackOverflow with the [`python-xarray` tag](https://stackoverflow.com/questions/tagged/python-xarray
+) or as a [GitHub discussion topic](https://github.com/pydata/xarray/discussions).
 
    If it’s easy to answer, feel free to link to the relevant documentation section, let them know that in the future this kind of question should be on StackOverflow, and close the issue.
 
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 59554f67891..81531965315 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -21,6 +21,10 @@ v2023.07.1 (unreleased)
 
 New Features
 ~~~~~~~~~~~~
+- Allow creating Xarray objects where a multidimensional variable shares its name
+  with a dimension. Examples include output from finite volume models like FVCOM.
+  (:issue:`2233`, :pull:`7989`)
+  By `Deepak Cherian <https://github.com/dcherian>`_ and `Benoit Bovy <https://github.com/benbovy>`_.
 
 
 Breaking changes
diff --git a/xarray/core/indexes.py b/xarray/core/indexes.py
index bfa8b9da07a..33b9b7bcff9 100644
--- a/xarray/core/indexes.py
+++ b/xarray/core/indexes.py
@@ -1645,7 +1645,7 @@ def default_indexes(
     coord_names = set(coords)
 
     for name, var in coords.items():
-        if name in dims:
+        if name in dims and var.ndim == 1:
             index, index_vars = create_default_index_implicit(var, coords)
             if set(index_vars) <= coord_names:
                 indexes.update({k: index for k in index_vars})
diff --git a/xarray/core/variable.py b/xarray/core/variable.py
index 720701be6f0..9d859c0d8a7 100644
--- a/xarray/core/variable.py
+++ b/xarray/core/variable.py
@@ -156,14 +156,8 @@ def as_variable(obj, name=None) -> Variable | IndexVariable:
             f"explicit list of dimensions: {obj!r}"
         )
 
-    if name is not None and name in obj.dims:
-        # convert the Variable into an Index
-        if obj.ndim != 1:
-            raise MissingDimensionsError(
-                f"{name!r} has more than 1-dimension and the same name as one of its "
-                f"dimensions {obj.dims!r}. xarray disallows such variables because they "
-                "conflict with the coordinates used to label dimensions."
-            )
+    if name is not None and name in obj.dims and obj.ndim == 1:
+        # automatically convert the Variable into an Index
         obj = obj.to_index_variable()
 
     return obj
diff --git a/xarray/testing.py b/xarray/testing.py
index dfd84851ac1..47e7dca81ae 100644
--- a/xarray/testing.py
+++ b/xarray/testing.py
@@ -364,14 +364,13 @@ def _assert_dataset_invariants(ds: Dataset, check_default_indexes: bool):
     assert all(
         ds._dims[k] == v.sizes[k] for v in ds._variables.values() for k in v.sizes
     ), (ds._dims, {k: v.sizes for k, v in ds._variables.items()})
-    assert all(
-        isinstance(v, IndexVariable)
-        for (k, v) in ds._variables.items()
-        if v.dims == (k,)
-    ), {k: type(v) for k, v in ds._variables.items() if v.dims == (k,)}
-    assert all(v.dims == (k,) for (k, v) in ds._variables.items() if k in ds._dims), {
-        k: v.dims for k, v in ds._variables.items() if k in ds._dims
-    }
+
+    if check_default_indexes:
+        assert all(
+            isinstance(v, IndexVariable)
+            for (k, v) in ds._variables.items()
+            if v.dims == (k,)
+        ), {k: type(v) for k, v in ds._variables.items() if v.dims == (k,)}
 
     if ds._indexes is not None:
         _assert_indexes_invariants_checks(
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 01c26ad6104..f7f91d0e134 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -35,6 +35,7 @@
 from xarray.core.indexes import Index, PandasIndex
 from xarray.core.pycompat import array_type, integer_types
 from xarray.core.utils import is_scalar
+from xarray.testing import _assert_internal_invariants
 from xarray.tests import (
     DuckArrayWrapper,
     InaccessibleArray,
@@ -467,13 +468,16 @@ def test_constructor(self) -> None:
 
         with pytest.raises(ValueError, match=r"conflicting sizes"):
             Dataset({"a": x1, "b": x2})
-        with pytest.raises(ValueError, match=r"disallows such variables"):
-            Dataset({"a": x1, "x": z})
         with pytest.raises(TypeError, match=r"tuple of form"):
             Dataset({"x": (1, 2, 3, 4, 5, 6, 7)})
         with pytest.raises(ValueError, match=r"already exists as a scalar"):
             Dataset({"x": 0, "y": ("x", [1, 2, 3])})
 
+        # nD coordinate variable "x" sharing name with dimension
+        actual = Dataset({"a": x1, "x": z})
+        assert "x" not in actual.xindexes
+        _assert_internal_invariants(actual, check_default_indexes=True)
+
         # verify handling of DataArrays
         expected = Dataset({"x": x1, "z": z})
         actual = Dataset({"z": expected["z"]})
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index a6dffb82660..9b70dcb5464 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -1247,8 +1247,10 @@ def test_as_variable(self):
         expected = Variable(("x", "y"), data)
         with pytest.raises(ValueError, match=r"without explicit dimension names"):
             as_variable(data, name="x")
-        with pytest.raises(ValueError, match=r"has more than 1-dimension"):
-            as_variable(expected, name="x")
+
+        # name of nD variable matches dimension name
+        actual = as_variable(expected, name="x")
+        assert_identical(expected, actual)
 
         # test datetime, timedelta conversion
         dt = np.array([datetime(1999, 1, 1) + timedelta(days=x) for x in range(10)])