How do I disable airplay?

It does not work that way.

There's nothing that needs to be done,

Your computer does not appear on anybody else's devices for Airplay, because you cannot AirPlay to computers. You AirPlay From computers only. You would only see Apple TVs you could AirPlay to if you specifically go looking for them in the AirPlay Menu when available.

If there is no Apple Tv to Airplay to the feature is simply not avaialble.

Computers should not be appearing there unless they have some type of AirPlay Receiver software installed, as out of the box you cannot AirPlay to a computer. If "Dan" has installed something, then conceivably you could start playing music to his computer and out of his speakers. But that's more on Dan than you,

There's really nothing you can do about it. Since you can't actually turn it off. Obviously the only entry that is yours is the My Computer option.

Other than that, you would recognize whatever name you gave to your devices as being yours. Hopefully something identifiable.