The site has always had an "Email" link below each user's avatar. Following this takes you to a form where you can write a message for that user.
Up until now, this message was delivered to the user's email account with the email you used to register on this site as the "From" address. I have added a checkbox that will use a site email address as the "From" address instead:

Of course, if you use this feature, the recipient of your message won't be able to reply to it and reach you. This is noted in the message. The recipient can instead use the site email feature to reach you, whether anonymously or not.