If named variables are replaced by unnamed ones, keep the name.

theano/compile/function_module.py

@@ -149,6 +149,9 @@ def std_env(input_specs, output_specs, accept_inplace = False):
 
     # We need to protect all immutable inputs from inplace operations.
     env.extend(Supervisor(input for spec, input in zip(input_specs, inputs) if not (spec.mutable or (hasattr(env, 'destroyers') and env.destroyers(input)))))
+
+    # If named nodes are replaced, keep the name
+    env.extend(gof.toolbox.PreserveNames())
     return env, map(SymbolicOutput, updates)
 
 class AliasedMemoryError(Exception):

theano/gof/toolbox.py

@@ -194,4 +194,7 @@ class PrintListener(object):
             print "-- changing (%s.inputs[%s]) from %s to %s" % (node, i, r, new_r)
 
 
-
+class PreserveNames:
+    def on_change_input(self, env, mode, i, r, new_r):
+        if r.name is not None and new_r.name is None:
+            new_r.name = r.name