Remove mirrored objects from an array

I have an issue which I dont’t really know how to tackle in a good way

I have an array of objects which looks roughly like this:

[
    { name: "horse", newName: "owl" }
    { name: "owl", newName: "horse" }
    { name: "frog", newName: "dog" }
]

I want to remove “mirrored” objects from this array, in result having an array like this:

[
    { name: "frog", newName: "dog" }
]

Basically I need to find objects with opposite keys and values

More complex scenarios:

[
    { name: "horse", newName: "frog" }
    { name: "owl", newName: "horse" }
    { name: "frog", newName: "owl" }
]

    // Result: []

[
    { name: "horse", newName: "frog" }
    { name: "dog", newName: "cat" }
    { name: "owl", newName: "horse" }
    { name: "frog", newName: "owl" }
    { name: "monkey", newName: "worm" }
    { name: "cat", newName: "dog" }
]

    // Result: [{ name: "monkey", newName: "worm" }]

In the first case I would simply loop through the array and if an object like this is found:

{key: obj1.value, value: obj1.key} I would splice them both

But I have no idea how to approach the more complex situation when 3 or more objects would have to be removed. Any hints?

In advance thanks for your time