What is a two-word phrase for: acquaintances about whom we know nothing

Solution 1:

The technical term for such acquaintances is

consequential strangers

Here is a description from NPR:

You get your coffee from your regular barista. You give a small nod to the guy you see every day at the gym. You don't know these people, but they're vital to your social landscape.

(http://www.npr.org/templates/story/story.php?storyId=112602248)

It's not a very common idiom, but it's an oxymoron, so it does fit your requirement of being ironic or playful.

Otherwise, there are the more common stock phrases:

distant acquaintances

passing acquaintances

nodding acquaintances (implying you know them only well enough to nod at, but not speak to)