No, you cannot. Once a public key is created, there's no way to change its private key. However, you can create a new account for the funds you own.
Ethereum, like Bitcoin, uses elliptic curves(ECs) to generate private/ public keys pairs. This might sound really complex, but, at the core, ECs are just functions which look like ...
The short answer is no, once the private key is created it always be the same. If you accidentally shared your private key somewhere you should create another account and transfer any value to the new account created (fast as possible)