I am used to calling this thing "covariance matrix" and only very rarely see and here it being called "variance-covariance matrix". However, our tag here is called variance-covariance. It used to slightly annoy me all the time, so I have recently created a tag covariance-matrix and voted to make it the synonym of the main tag. The voting has not finished yet$^*$, but in the meantime I see that my newly created tag is being used by other people.
This makes me wonder: shall we maybe have covariance-matrix as the master tag, and variance-covariance as its synonym? I tried some google searches to establish the usus:
"covariance matrix" search gives 3 mln results, and
"variance-covariance matrix" only 400k (this is included in 3 mln too). On google scholar the numbers are 900k and 100k respectively. So it seems that "covariance matrix" is indeed a more common expression used over 80% of the times.
I am going to post two answers, please upvote the one with your preferred master tag.
$^*$The voting is likely to never finish; apart from me, only one single person (@gung) has taken part in it so far. Sad as it is, we will need a moderator to create this synonym one way or another.