One that isn't insulting to the liberals that exist under the "progressive" tent? I don't know. The word is essentially a tent of social-democrats and socialists, and that tent is useful as an alliance but damaging in that it erases socialists from discourse as they get consumed into "progressive liberals". This erasure results in fewer people learning the difference between socialists and liberals, in fact it makes people think socialists are liberals.

Socialists should call themselves socialists and any big-tent collaboration should be clearly labelled as a Socialist-LeftLiberal collaboration/alliance.

The benefit of calling someone like Bernie or AOC LeftLiberal instead of Progressive is it educates less political people that LeftLiberal and RightLiberal exists. This pushes the vast majority of the Democrats to the right in people's minds and it will open up space for a "left" to exist. While doing this it also clearly educates people that Socialists and LeftLiberals are not the same thing.

You get me? If LeftLiberal becomes a thing in people's minds then everything that is not LeftLiberal becomes right wing in people's minds, pushing the entirety of the democrat party into the right and opening up control of what "left" exists to Socialists and Social Democrats. The benefit of this is that everyone who currently associates "left" with being good will fall into this camp over time, they will reject RightLiberals when they become associated with being right wing in their minds. So much american thinking can be boiled down to "left good, right bad" or "right good, left bad". This can be weaponised linguistically.

It is possible to convince LeftLiberals to start doing this because they will realise how much it benefits them to make the distinction. And it is possible to convince Socialists to start doing this because it stops erasing Socialists.