Is it possible to "reserve" a private key? In other words, can someone select a private key and perform an action (such as creating a specific transaction or something else) that effectively claims or reserves that key?
Nope. Private keys are randomly generated, and you can't pick a certain private key for you to keep. What you get is what your private key and for you to own this you need to make sure that you keep your private keys and keep it secure. If someone gets ahold of your private keys then they will have access on your wallet and your funds. What do you even want to do that you want to reserve a private key? Are you aiming for aesthetic or what? Is it for branding?