diff --git a/mathics/eval/assignments/assignment.py b/mathics/eval/assignments/assignment.py
index b956fa27b8..3bf9151744 100644
--- a/mathics/eval/assignments/assignment.py
+++ b/mathics/eval/assignments/assignment.py
@@ -471,11 +471,15 @@ def eval_assign_format(
         ]
     lhs = lhs.elements[0]
     lhs_unwrapped = unwrap_expression(lhs)
-    lhs_unwrapped = (
-        lhs_unwrapped.get_head()
-        if not isinstance(lhs_unwrapped, Symbol)
-        else lhs_unwrapped
-    )
+    # For a named pattern or a blank, as in Format[t_h] or Format[_h],
+    # keep the pattern: the tag is h, which is found inside it below.
+    # Otherwise, the tag is the head, as in Format[h[x_]].
+    if not (
+        isinstance(lhs_unwrapped, Symbol)
+        or lhs_unwrapped.has_form(SymbolPattern, 2)
+        or lhs_unwrapped.get_head() in BLANK_PATTERN_HEADS
+    ):
+        lhs_unwrapped = lhs_unwrapped.get_head()
     target_symbol_names = collect_lhs_names_and_upset_dont_allow_custom(
         target_symbol_names, upset, op_name, lhs, lhs_unwrapped, evaluation
     )
diff --git a/test/builtin/assignments/test_assignment.py b/test/builtin/assignments/test_assignment.py
index 16ea2bae4c..dc80a65f8f 100644
--- a/test/builtin/assignments/test_assignment.py
+++ b/test/builtin/assignments/test_assignment.py
@@ -178,6 +178,22 @@ def test_assign_list():
             '"{2, a}"',
             "store the conditional rule for T...",
         ),
+        # Named patterns and blanks as the argument of Format
+        (
+            'ClearAll[A,G]; Format[A_G]:="g" /; Length[A] > 1; {G[1,2], G[1]}//ToString',
+            '"{g, G[1]}"',
+            "Format[A_G] is stored for G, not for Pattern",
+        ),
+        (
+            'ClearAll[G]; Format[_G]:="g"; G[1]//ToString',
+            '"g"',
+            "Format[_G] is stored for G",
+        ),
+        (
+            'ClearAll[t,G]; Format[t:G[__]]:="g"; G[1]//ToString',
+            '"g"',
+            "Format[t:G[__]] is stored for G",
+        ),
         # Upvalues
         (
             "ClearAll[F,A,Y,x]; A=T; F[A[x_],Y[x_]]^:=x^2; ClearAll[A,F,Y]; F[T[2],Y[2]]",