A mortise is a slot or recess, usually with flat sides. In joinery, a mortise usually receives a matching tenon. If the joint goes all the way through the workpiece, it is a "through mortise"; if only part way, a "blind mortise".
Since the English language doesn't have a generic word for "something cut with a router" but instead uses "routed" as an adjective to describe the specific thing so cut, it sounds from your description like your anvil sits in a "routed recess". However, given that that recess is designed to join together your anvil and its base, it is appropriate to call it a mortise or to say that your anvil is "mortised into" the stump.
Just to be clear: this isn't meant as personal criticism. I'm just trying to make sure that we're all on the same page, so far as vocabulary is concerned. English is tricky enough, even before we get into the obscure terminology of specialized crafts.