The service I was writing about is French: http://www.service-virtualis.com/virtualis/index.htm

So unfortunately if you get points I'm guessing you're from North America and probably won't be able to apply.

I haven't searched but there might be such services available to you in a nearer bank.

I've done it with a Citi Double Cash card. It's a nice all around card: 2% cash back, price matching, temporary numbers, etc. Don't take my recommendation blindly though, do your own research first of course!

Edit: As a meta-sidenote, it was very difficult for me to write this comment without feeling like it would come across as corporate shilling. I have no connection to Citi and nothing to gain from recommending their card, but there's no way for anybody else to know that, and the issue of selling old accounts is a real one (though don't know about HN specifically). I wonder what the best solutions are to this sort of issue.

Bank of America credit cards have this, they call it ShopSafe. My old Citi card had that although I can’t verify they still offer it. I believe Capital One has virtual credit card number capability as well.

US market here... Citi card. For many reasons, I loathe Citi and would like to drop using them, but I keep this card for this one feature.

I did this strategy just today with privacy.com which isn't a credit card at all but bills your bank account directly.

All the citibank cards can generate Virtual Account Numbers with time and dollar limits. I use them frequently.