diff --git a/tests/test_merge.py b/tests/test_merge.py
index 69e8301..aae3db1 100644
--- a/tests/test_merge.py
+++ b/tests/test_merge.py
@@ -29,7 +29,7 @@ def mdata():
 
 @pytest.mark.usefixtures("filepath_h5mu", "filepath_zarr")
 class TestMuData:
-    def test_merge(self, mdata, filepath_h5mu):
+    def test_merge(self, mdata):
         mdata1, mdata2 = mdata[:N1, :].copy(), mdata[N1:, :].copy()
         mdata_ = mudata.concat([mdata1, mdata2])
         assert list(mdata_.mod.keys()) == ["mod1", "mod2"]
diff --git a/tests/test_update.py b/tests/test_update.py
index f475687..e6a37f4 100644
--- a/tests/test_update.py
+++ b/tests/test_update.py
@@ -218,6 +218,33 @@ def test_update_after_obs_reordered(self, mdata):
             [all(true_obsm_values[i] == test_obsm_values[i]) for i in range(len(true_obsm_values))]
         )
 
+    @pytest.mark.parametrize("obs_mod", ["unique"])
+    @pytest.mark.parametrize("obs_across", ["intersecting"])
+    @pytest.mark.parametrize("obs_n", ["joint", "disjoint"])
+    def test_update_intersecting_var_names_after_filtering(self, mdata):
+        orig_shape = mdata.shape
+        mdata.mod["mod1"].var_names = [str(i) for i in range(mdata["mod1"].n_vars)]
+        mdata.mod["mod2"].var_names = [str(i) for i in range(mdata["mod2"].n_vars)]
+        mdata.update()
+        mdata.mod["mod1"] = mdata["mod1"][:, :5].copy()
+        mdata["mod1"].var["true"] = True
+        mdata["mod2"].var["false"] = False
+        assert mdata["mod1"].n_vars == 5
+        mdata.update()
+        mdata.pull_var(prefix_unique=False)
+        assert mdata.n_obs == orig_shape[0]
+        assert mdata.n_vars == mdata["mod1"].n_vars + mdata["mod2"].n_vars
+        assert mdata.var["true"].sum() == 5
+        assert (~mdata.var["false"]).sum() == (~mdata["mod2"].var["false"]).sum()
+
+    @pytest.mark.parametrize("obs_mod", ["unique"])
+    @pytest.mark.parametrize("obs_across", ["intersecting"])
+    @pytest.mark.parametrize("obs_n", ["joint", "disjoint"])
+    def test_update_to_new_names(self, mdata):
+        mdata["mod1"].var_names = [f"_mod1_var{i}" for i in range(1, mdata["mod1"].n_vars + 1)]
+        mdata["mod2"].var_names = [f"_mod2_var{i}" for i in range(1, mdata["mod2"].n_vars + 1)]
+        mdata.update()
+
 
 # @pytest.mark.usefixtures("filepath_h5mu")
 # class TestMuDataSameVars: