Is it normal to want to be someone’s pet?

This means you are an airhead, have a lot of time in your hands. That gives you the luxury to imagine such ideas. Let's trade places for a day.

Many people won't see it as normal because it's often considered perverted (and truth be told it kinda is), but having a BDSM relationship is definitely normal within reason. You might simply have a fondness for being disciplined or have a high fondness for having someone set boundaries and rules for you. Either way, it's not exactly inherently unnormal for you to be into that sort of thing.

Blech, why would anyone want to own another human being? I wouldn't even want a monkey, or an ape, much less a human being.

I don't care what anyone says, when you're legally married to someone, they own you. And vice versa. So just get hitched. Bada-bing.

Very normal

sounds like some sort of weird BDSM fantasy.