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?
Apart from the fact that it's not possible to reserve it, what do you want to achieve?
A private key is the way to sign bitcoin transactions. If there is a private key X and there are 10 people that know it, then whoever uses it first will eventually get the coins.
So, even if you "reserved" the key, even though I don't know what "reserve" means, if anyone got the key they would be able to steal your funds.
The good thing though, is that if you protect your private key correctly, you are guarranteed to be the only one to own it, hence, you can reserve it without doing anything.