PayPal adds this greeting to the currently-cookied user on your machine. If you begin the checkout, PayPal will query your (the currently-cookied user) account to begin the checkout process, and depending upon the outcome of security checks may even permit you to check out without logging in again for each payment.
"Eugene" is probably the name on one of your sandbox accounts. PayPal sees that cookie even when running live transactions, but would (of course) not actually permit the sandbox account to make live transactions; when "real" PayPal code runs (once the button is clicked) the sandbox account information would be rejected and the user will be prompted to log in.
This is one of several ways that sandbox and live PayPal cookies can interact a bit oddly; fortunately none of these interactions are fatal and they generally only affect you the developer; your customers will generally not have PayPal sandbox accounts cookied on their computer.
And just as some confirmation, running the provided snippet on my machine does not greet Eugene :).