diff --git a/symengine/lib/symengine_wrapper.in.pyx b/symengine/lib/symengine_wrapper.in.pyx
index 8974b7d9..06b85266 100644
--- a/symengine/lib/symengine_wrapper.in.pyx
+++ b/symengine/lib/symengine_wrapper.in.pyx
@@ -2412,8 +2412,15 @@ class Pow(Expr):
 class Function(Expr):
 
     def __new__(cls, *args, **kwargs):
-        if cls == Function and len(args) == 1:
-            return UndefFunction(args[0])
+        if cls == Function:
+            nargs = len(args)
+            if nargs == 0:
+                raise TypeError("Required at least one argument to Function")
+            elif nargs == 1:
+                return UndefFunction(args[0])
+            elif nargs > 1:
+                raise TypeError(f"Unexpected extra arguments {args[1:]}.")
+
         return super(Function, cls).__new__(cls)
 
     @property
@@ -2834,6 +2841,10 @@ class FunctionSymbol(Function):
         name = deref(X).get_name().decode("utf-8")
         return str(name)
 
+    @property
+    def name(Basic self):
+        return self.get_name()
+
     def _sympy_(self):
         import sympy
         name = self.get_name()
diff --git a/symengine/tests/test_functions.py b/symengine/tests/test_functions.py
index 3a19b122..207add98 100644
--- a/symengine/tests/test_functions.py
+++ b/symengine/tests/test_functions.py
@@ -103,6 +103,18 @@ def test_derivative():
     assert i == fxy.diff(y, 1, x)
 
 
+def test_function():
+    x = Symbol("x")
+    fx = Function("f")(x)
+    assert fx == function_symbol("f", x)
+
+    raises(TypeError, lambda: Function("f", "x"))
+    raises(TypeError, lambda: Function("f", x))
+    raises(TypeError, lambda: Function())
+
+    assert fx.name == "f"
+
+
 def test_abs():
     x = Symbol("x")
     e = abs(x)