diff --git a/pytensor/graph/basic.py b/pytensor/graph/basic.py
index 512f0ef3ab..6dc297e33d 100644
--- a/pytensor/graph/basic.py
+++ b/pytensor/graph/basic.py
@@ -270,11 +270,11 @@ def clone_with_new_inputs(
 
         # Some Ops like Alloc require the node to always be rebuilt in non-strict mode
         # as the output type depends on the input values and not just their types
-        output_type_depends_on_input_value = self.op._output_type_depends_on_input_value
+        data_dependent_output_shape = self.op.data_dependent_output_shape
 
         for i, (curr, new) in enumerate(zip(self.inputs, new_inputs, strict=True)):
             # Check if the input type changed or if the Op has output types that depend on input values
-            if (curr.type != new.type) or output_type_depends_on_input_value:
+            if (curr.type != new.type) or data_dependent_output_shape:
                 # In strict mode, the cloned graph is assumed to be mathematically equivalent to the original one.
                 # We only need to rebuild a node when the new input has a different, but compatible, type.
                 # This can happen e.g., when we provide a new input with a more specialized static shape.
diff --git a/pytensor/graph/op.py b/pytensor/graph/op.py
index 690bb44df5..db90b348c1 100644
--- a/pytensor/graph/op.py
+++ b/pytensor/graph/op.py
@@ -195,7 +195,7 @@ class Op(MetaObject):
     itypes: Sequence["Type"] | None = None
     otypes: Sequence["Type"] | None = None
 
-    _output_type_depends_on_input_value = False
+    data_dependent_output_shape = False
     """
     Whether the static output type depends on the inferred value of one of the inputs.
     (e.g, via constant folding or static shape inference).
diff --git a/pytensor/tensor/basic.py b/pytensor/tensor/basic.py
index 26bd34692b..b981679823 100644
--- a/pytensor/tensor/basic.py
+++ b/pytensor/tensor/basic.py
@@ -1362,7 +1362,7 @@ def triu_indices_from(
 
 
 class Eye(Op):
-    _output_type_depends_on_input_value = True
+    data_dependent_output_shape = True
     __props__ = ("dtype",)
 
     def __init__(self, dtype=None):
@@ -1577,7 +1577,7 @@ class Alloc(COp):
     """
 
     _f16_ok = True
-    _output_type_depends_on_input_value = True
+    data_dependent_output_shape = True
 
     __props__ = ()
 
@@ -4213,7 +4213,7 @@ def perform(self, node, inputs, outputs):
 class AllocEmpty(COp):
     """Implement Alloc on the cpu, but without initializing memory."""
 
-    _output_type_depends_on_input_value = True
+    data_dependent_output_shape = True
 
     __props__ = ("dtype",)
     params_type = ParamsType(typecode=int32)
diff --git a/pytensor/tensor/random/op.py b/pytensor/tensor/random/op.py
index c76d250c9e..b20b96cea3 100644
--- a/pytensor/tensor/random/op.py
+++ b/pytensor/tensor/random/op.py
@@ -41,7 +41,7 @@ class RandomVariable(Op):
 
     """
 
-    _output_type_depends_on_input_value = True
+    data_dependent_output_shape = True
 
     __props__ = ("name", "signature", "dtype", "inplace")
     default_output = 1
diff --git a/pytensor/tensor/shape.py b/pytensor/tensor/shape.py
index 8913d6fb4d..38bda6fb61 100644
--- a/pytensor/tensor/shape.py
+++ b/pytensor/tensor/shape.py
@@ -398,7 +398,7 @@ class SpecifyShape(COp):
     view_map = {0: [0]}
     __props__ = ()
     _f16_ok = True
-    _output_type_depends_on_input_value = True
+    data_dependent_output_shape = True
 
     def make_node(self, x, *shape):
         x = ptb.as_tensor_variable(x)
@@ -619,7 +619,7 @@ class Reshape(COp):
 
     view_map = {0: [0]}  # output 0 is potentially aliased to inputs [0]
     _f16_ok = True
-    _output_type_depends_on_input_value = True
+    data_dependent_output_shape = True
 
     check_input = False
     __props__ = ("ndim",)