They don't even call themselves that any more - they try out new slogans and memes and they all are shit, but by producing more and more shit, they make more shit for the shit god, more puke for the puke throne.
Anyway, there hasn't been a substantive "left" for a long time. What they wound up doing in the Soviet Union diverged from "leftism" and was trying to maintain international relevance without any real idea or goal except survival. You can't blame them - history gave them a shitty deal. They really had a hard time holding it together outside of the core, and they were running on defeating the Nazis for as long as they could. So, "the left" as an oppositional force against the ruling interests or even something that could contest it was pretty well dead by the 1970s. The last embers of it were extinguished during the 1960s and it was pretty quickly papered over with the student movement, because that was the core of the left and they got everything they wanted by promoting their institution above everything else. The last avenues for the working class to conceive of a world where they could be anything but oppressed serfs would be cut, and the institutions became so alien to them that it's like dealing with an alien species - and this is the intended effect of so much that happened in the past century.
That said, the left and right still "exist" - that is still the core contention in the political arena. The right won so hard that it hurts, but the left still exists as the loyal opposition to be kicked around, and there isn't a divergent thought from anything that has been permitted in the global discourse. The replacement of leftism and rightism with ideology and feels > reals warped the historical positions of the right and left, and it has been a deliberate mindfuck to "give" the right populist and anti-institutional positions while saddling the center-left and left proper with the association with eugenics, population control, and these institutions that nearly everyone recognizes as the chief threat in their life. The right in all final decisions will rally behind the institutions - they merely insist on purging them of any "left" elements, and for the vanguard, they thought Eisenhower was a far leftist, to give you an idea of how much the right pushes its agenda. Pretty much everything they call "politics" today has nothing to do with the genuine animal, or the actual positions of the right and left, but the struggle to control the institutions very much carries on that struggle between the prerogatives of the state and the interests of the institutions and membership. So far as the left has a genuine existence, it fought over legal rights, civil rights, and what remained of the public interest in the institutions. Those struggles were not for nothing. We have seen in the past 20 years what it is like to live in a world where there is no such thing as a legal right, and it fucking sucks.