For me it was possible, I have my own Pasmo that's personalized; but I got that card few years back so from that page it seems to me the interface has been updated.
Generally if a number is needed a Japanese number is needed. You'll probably not need a personalized card if you're not planning to go back to Japan within 10 years, as the card expires in 10 years upon non usage. A non personalized Pasmo should be safe enough unless you do not place your card in your wallet or something. I've ever tried losing my 2 day metro pass when it fell out of my pocket when I retrieved my wallet, but you'll be safe if you keep the card in your wallet. Scanners are able to detect Pasmo cards in wallets even if you have a credit card in there, unlike Singapore gantries which fail if you have a credit card in your wallet and you try to tap the entire wallet.