... mention what the actual name of the business ...
Maybe they want to avoid disturbing their customer base. People who already have pending work or people who are about to place orders would assume that the original proprietor was going to do the work.
It's a fun subject for discussion, and I've got a guess, but I think it might be a bad idea to speculate about it online. I don't want to start any rumors or cause any builder distress, and it's only a guess. The seller clearly doesn't want to go public yet, but an add like can only make us wonder.
p****footing around the name of your business, & claiming it's worth XX amount strikes me as some kind of clickbait/scam. As far as customer sensitivities go, it should be well known by all adults that It's the nature of capitalism & companies to close/sell & move on. If one was really looking for a buyer, the reputation & name of the enterprise would be put to the fore. (I may be proven wrong in the future, but for now, this AD makes no sense).
(As an aside, I noticed that my last post had a word altered, because of the unsophistication of the censoring program of this website. The idiom "p****footing" originated from the observation of the stealthy movements of a cat, & the consequent meaning of avoiding a subject).
As bill-e said earlier, I have a guess. It makes sense, but I won’t speculate at ths point. I focused on the “old-time,” which eliminates Nechville and the various bluegrass banjo makers. I also noted “established,” but not “long-established.” Not many other clues though.
As someone who has a day job with a small company in a specialized market, I've learned that sometimes it is worthwhile to buy a competitor to take them (and their tooling) out of competition.