I think I've only given a pet name to one such thing in my life. It's my oldest and most beloved stuffed animal. It's a ray(like the fish) called "The Ray" or "Ray-y" ("Rockan" in Swedish.). He looks sort-of like the one in the picture but fatter.

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Outside of that I don't really give names to things. My computer is called Gizmo but it's not like I refer to it as "Gizmo", it's just my computer.