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?
Definitely not for branding, since
1. Private key should remain private or not shared.
2. There's avalanche effect when you convert public key to Bitcoin address due to hashing cryptography. And AFAIK avalanche effect also happens when you generate public key from private key.
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?
~ Acknowledged, this my post was deleted my the moderator due to inappropriate quote. I'm reposting after corrected. Pardon in case of unlawfulness.
Yes you can generate your own private wallet keys depending on your choice of wallet though but if I'd advice you, it's risky in generating multiple private keys as reserved. Remember that the network generated private keys are still yours which security mechanism is the same even when you create a personal one as you assumed to be reserve.
The risky about taking this action is that you'd be protecting two sides wallet private keys and which means managing to keep it secured would give you additional tasks.
You can only reserve your private keys basically on places you can easily get reach to them in different places but be sure not to set it out of reach of any other person.
So let go your thought of creating that so reserved private keys to enhance your private keys storage secured.
1. Bitcoin network doesn't generate private key specifically for you.
2. Bitcoin protocol doesn't offer any feature to reserve private key.