Your premise is false on its face, and that renders your argument null and void.
That's not what "the left" is doing. At all.
You're also confusing an opposition to monuments which celebrate individuals whose entire careers were in support of horror and human rights atrocities, with the name on an organization that bears essentially no ideological similarity with an earlier form of the same thing.
It's the ideological continuity that matters, and that simply does not exist with the Democratic Party.