For me, "Max" is too general, and I feel for Cinemax, who've used "Max" in their name for so long. Hahaha. "Warner Max" would've been the right name, focusing on HBO & Discovery-owned programming. And you're right: NBC had it right with "Peacock", because the peacock was also synonymous with NBC's logo dating back to 1956 (ended in 1975 and returned in 1979). Just like the eye has always been synonymous with CBS. It's a missed opportunity, but, like I said, so long as the content is the same (HBO Max to Max), then I am happy, because the film content is top tier, and the quality is amazing.
The fact Discovery+ isn't ending is infuriating to me, because they don't want to lose that customer base. Let them go to Max like HBO Max people need to move.