In my opinion, choosing the name Hive was a mistake, not a deadly mistake, but not a very well thought-out decision. I'm not sure about this, but I guess it was done in a rush? And maybe no one Googled the term "Hive Blockchain" before settling for this name?
Something that I noticed is that communities already had the previous "hive" even before the fork; maybe that's why Hive was chosen.
Having said that, Steem was not the best name. Most people, when they heard it, confused it with "Steam", the video game platform from Valve.
I think that an uncommon name would have been better. An invented word, something that many companies have done (Google, Yahoo, etc.). Hive is a word that is very common, and it could even have a negative sentiment attached to it. "The Hive" is actually a criminal group in DC comics. It is also a very common word in the tech industry.
I do think that this has damaged our organic growth, as you mention, and even LLMs many times can't distinguish between "Hive Blockchain" and "Hive Digital Technologies".
This was a long comment to say, yes. I would support a rebrand.
RE: Support for Hive Rebrand (In Principle)