diff --git a/pytensor/graph/basic.py b/pytensor/graph/basic.py
index 29b2043f6d..3d94ce83b7 100644
--- a/pytensor/graph/basic.py
+++ b/pytensor/graph/basic.py
@@ -616,16 +616,20 @@ def eval(
         """
         from pytensor.compile.function import function
 
+        ignore_unused_input = kwargs.get("on_unused_input", None) in ("ignore", "warn")
+
         def convert_string_keys_to_variables(inputs_to_values) -> dict["Variable", Any]:
             new_input_to_values = {}
             for key, value in inputs_to_values.items():
                 if isinstance(key, str):
                     matching_vars = get_var_by_name([self], key)
                     if not matching_vars:
-                        raise ValueError(f"{key} not found in graph")
+                        if not ignore_unused_input:
+                            raise ValueError(f"{key} not found in graph")
                     elif len(matching_vars) > 1:
                         raise ValueError(f"Found multiple variables with name {key}")
-                    new_input_to_values[matching_vars[0]] = value
+                    else:
+                        new_input_to_values[matching_vars[0]] = value
                 else:
                     new_input_to_values[key] = value
             return new_input_to_values
diff --git a/tests/graph/test_basic.py b/tests/graph/test_basic.py
index 08c352ab71..84ffb365b5 100644
--- a/tests/graph/test_basic.py
+++ b/tests/graph/test_basic.py
@@ -367,6 +367,10 @@ def test_eval_kwargs(self):
             self.w.eval({self.z: 3, self.x: 2.5})
         assert self.w.eval({self.z: 3, self.x: 2.5}, on_unused_input="ignore") == 6.0
 
+        # regression test for https://github.com/pymc-devs/pytensor/issues/1084
+        q = self.x + 1
+        assert q.eval({"x": 1, "y": 2}, on_unused_input="ignore") == 2.0
+
     @pytest.mark.filterwarnings("error")
     def test_eval_unashable_kwargs(self):
         y_repl = constant(2.0, dtype="floatX")