diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 248f516b61b..3c86bd504cf 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -4393,16 +4393,18 @@ def swap_dims(
         # rename_dims() method that only renames dimensions.
 
         dims_dict = either_dict_or_kwargs(dims_dict, dims_kwargs, "swap_dims")
-        for k, v in dims_dict.items():
-            if k not in self.dims:
+        for current_name, new_name in dims_dict.items():
+            if current_name not in self.dims:
                 raise ValueError(
-                    f"cannot swap from dimension {k!r} because it is "
+                    f"cannot swap from dimension {current_name!r} because it is "
                     f"not one of the dimensions of this dataset {tuple(self.dims)}"
                 )
-            if v in self.variables and self.variables[v].dims != (k,):
+            if new_name in self.variables and self.variables[new_name].dims != (
+                current_name,
+            ):
                 raise ValueError(
-                    f"replacement dimension {v!r} is not a 1D "
-                    f"variable along the old dimension {k!r}"
+                    f"replacement dimension {new_name!r} is not a 1D "
+                    f"variable along the old dimension {current_name!r}"
                 )
 
         result_dims = {dims_dict.get(dim, dim) for dim in self.dims}
@@ -4412,24 +4414,24 @@ def swap_dims(
 
         variables: dict[Hashable, Variable] = {}
         indexes: dict[Hashable, Index] = {}
-        for k, v in self.variables.items():
-            dims = tuple(dims_dict.get(dim, dim) for dim in v.dims)
+        for current_name, current_variable in self.variables.items():
+            dims = tuple(dims_dict.get(dim, dim) for dim in current_variable.dims)
             var: Variable
-            if k in result_dims:
-                var = v.to_index_variable()
+            if current_name in result_dims:
+                var = current_variable.to_index_variable()
                 var.dims = dims
-                if k in self._indexes:
-                    indexes[k] = self._indexes[k]
-                    variables[k] = var
+                if current_name in self._indexes:
+                    indexes[current_name] = self._indexes[current_name]
+                    variables[current_name] = var
                 else:
                     index, index_vars = create_default_index_implicit(var)
                     indexes.update({name: index for name in index_vars})
                     variables.update(index_vars)
                     coord_names.update(index_vars)
             else:
-                var = v.to_base_variable()
+                var = current_variable.to_base_variable()
                 var.dims = dims
-                variables[k] = var
+                variables[current_name] = var
 
         return self._replace_with_new_dims(variables, coord_names, indexes=indexes)