You can have a little fun. No, you can't identify or email the scammer in these cases. As you probably know, their goal is to get you to "login" to paypal using their fake website; this allows them to capture your ID / password. I always go to their fake website to login. Here are my credentials:
Username:
JustWanted@To.Say
password: PhuckYouScammer
I get the satisfaction of knowing that they WILL see this on their server.
Meanwhile, regarding paypal security ... everyone should have 2-factor authentication on all their accounts (all the ones that offer it) such as Amazon, eBay, PayPal, your bank, your brokerage, etc. A code is sent to your phone when you attempt to login which you then have to provide in order to proceed.
Even if some scammer got a password to your account, they are stopped dead because they don't have access to your phone and this one-time code. PLUS, if you get a code on your phone for Paypal (example) and it's not you trying to login, you have an immediate alert that your password has been compromised. But, relax ... nothing urgent ... no need to panic - they can't get in without the code. So, just go change your password after you finish your round of golf and take a shower.
I even put 2-factor on my email. Why? Because email is the primary method for password change / recovery; especially for accounts that don't offer 2-factor (yet). So, even if a hacker tried to do a password reset for my grocery delivery account and even if they had my email password, they could not possibly proceed because they can't even get into my email (no code) to complete the process.