diff --git a/python/torch_mlir/extras/fx_importer.py b/python/torch_mlir/extras/fx_importer.py
index 91f3c27ee263..e6d0f03deda4 100644
--- a/python/torch_mlir/extras/fx_importer.py
+++ b/python/torch_mlir/extras/fx_importer.py
@@ -623,7 +623,7 @@ def import_program(
         node_importer.return_node_values(loc, user_outputs)
         self.symbol_table.insert(func_op)
 
-    def import_frozen_program(self, prog: torch.export.ExportedProgram):
+    def import_frozen_program(self, prog: torch.export.ExportedProgram, func_name: str = "main"):
         """Imports a consolidated torch.export.ExportedProgram instance.
 
         If using the new torch.export path (vs a lower level precursor), then this is
@@ -702,7 +702,7 @@ def import_frozen_program(self, prog: torch.export.ExportedProgram):
                 node.replace_all_uses_with(replacement)
                 g.erase_node(node)
 
-        self.import_stateless_graph(g)
+        self.import_stateless_graph(g, func_name)
 
     def import_graph_module(self, gm: GraphModule):
         """Low-level import of a GraphModule assuming that it has been functionalized.
diff --git a/python/torch_mlir/fx.py b/python/torch_mlir/fx.py
index 1f5aa8f74add..76cd91f82e0a 100644
--- a/python/torch_mlir/fx.py
+++ b/python/torch_mlir/fx.py
@@ -23,6 +23,7 @@ def export_and_import(
     constraints: Optional[torch.export.Constraint] = None,
     experimental_support_mutation: bool = False,
     hooks: Optional[FxImporterHooks] = None,
+    func_name: str = "main",
     **kwargs,
 ):
     context = ir.Context()
@@ -36,8 +37,8 @@ def export_and_import(
     if experimental_support_mutation:
         if torch.__version__ < "2.3.0.dev20240207":
             warnings.warn("Mutable program import only supported on PyTorch 2.3+")
-        fx_importer.import_program(prog)
+        fx_importer.import_program(prog, func_name=func_name)
     else:
-        fx_importer.import_frozen_program(prog)
+        fx_importer.import_frozen_program(prog, func_name=func_name)
 
     return fx_importer.module_op
diff --git a/test/python/fx_importer/basic_test.py b/test/python/fx_importer/basic_test.py
index 36c554862506..fc5b2030b648 100644
--- a/test/python/fx_importer/basic_test.py
+++ b/test/python/fx_importer/basic_test.py
@@ -56,3 +56,24 @@ def forward(self, x):
 
     m = fx.export_and_import(Basic(), torch.randn(3, 4))
     print(m)
+
+
+@run
+# CHECK-LABEL: test_import_frozen_exported_program_with_func_name
+# CHECK:     func.func @test_net(%[[ARG0:[a-zA-Z0-9]+]]: !torch.vtensor<[3,4],f32>) -> !torch.vtensor<[3,4],f32>
+def test_import_frozen_exported_program_with_func_name():
+    @torch._dynamo.assume_constant_result
+    def get_a():
+        return torch.randn(1, 4)
+
+    class Basic(nn.Module):
+        def __init__(self):
+            super().__init__()
+            self.b = torch.randn(3, 1)
+            self.p = nn.Parameter(torch.randn(1, 1))
+
+        def forward(self, x):
+            return torch.tanh(x) * get_a() * self.b * self.p
+
+    m = fx.export_and_import(Basic(), torch.randn(3, 4), func_name="test_net")
+    print(m)