Great step, but I'd prefer the title being less specific- "medicare for all" is just one way to achieve a universal healthcare system. You could have a public option or a system which isn't exactly single payer but also not multi payer but guarantees healthcare (such as we have in Israel). Dems should be open to ideas- I'd prefer it named "Universal Healthcare Caucus".
Having a Universal Healthcare caucus would be redundant, because there are only 5 people in the democratic party who aren't in favor of something in that range. You might as well say "Democratic caucus 2" at that point.
Don't like M4A, argue the merits of the M4A caucus' existence, not about phrasing. Ambivalent about it, same thing.
Unrelated, but to anyone complaining about Medicare for all being called Medicare for all, American political linguistics have been garbage for decades and no amount of re-appropriation of words is going to change that. Notable examples of silly Americanisms are "liberal" meaning left or left-leaning, and the existence of the phrase "family values". Once Americans have decided that they want a certain phrase or word to reference a specific thing, you're pretty much screwed if you don't like it.