What is this plant?

We inherited this plant from the previous owners of our flat. It seems to be flourishing in the garden, but I have no idea what it is, and I don’t know how to check either, so any ideas / solutions would be greatly appreciated!

Also any tips on what to do with it at this time of year when it’s looking a little bit sad would be good. Does it need chopping back, or mulching, or just leaving in peace? Your infinite collective wisdom is welcomed.