Shepherd’s pie: minced lamb with mashed potato topping. I suppose that is a logical name although I would be surprised if shepherds are often encouraged to eat their flocks.
Cottage pie: minced beef with a mashed potato topping. I guess people in cottages often eat this, but the link is even more tenuous.
So, what would you call a mash-topped pie made with a veggie filling? I blitzed onions in a food processor and set them softening, then added a blitzed mixture of mushroom, courgettes, peppers and garlic. Proper vegetarians would probably not smile kindly on the Oxo cube (nor vegans on the egg that, along with leftover ‘Mexican houmus’, enhanced the mash) but it was a pretty tasty result however it ought to be named.