I understand your point, but I would think that "future shareholders" involve two separate categories of people, neither of which are really influenced by the name change.
Don't know if you own much stock, but future shareholders don't shop around for stocks to purchase based solely on the parent company name. Not successful stock trader's anyway. Successful ones will see a new name pop up and do some research on their earnings-history, guidance, and publish innovations pushing growth. I know of zero successful investors in Wall Street who look solely at a name and say, they'll pass. Maybe the old day-traders of the early 90's buying penny stocks in bulk would have, but with all the automated trading being used today, those days are long gone.
The first category is the 401K holder and mutual fund holder, who probably couldn't tell you what companies are in their portfolio on any given day, much less whether any of them changed their name. And the second category is the expert, who probably knows the ins and outs of the company regardless of the name of it. A name isn't going to make them buy stock if they think the company is poorly run.
Most people with 401K's choose to let the investment company manage their portfolio. Sure, you can re-balance by choosing stocks over bonds, conservative over more aggressive, domestic or foreign investments. Very few actually drill down into choosing individual stocks and number of shares involved in their 401K.
If a company is a retail store, or a brand that directly sells services or goods to the public, yeah, a brand name change sometimes can help with sales or visibility. But most users of Entercom's services don't know it exists. They know it as "KISW" (in Seattle).
At a granular-brand level that's correct. I'm willing to bet that 99.9% of the listeners don't know that KISW is owned by Entercom or Rubber Dog Poo. You probably use hundreds of different products daily or weekly, that you only know the product name, not the parent company.
Expert stockholders are more concerned about the operation, the running of the company, and its financials, as opposed to the name on the door. The name on the door means nothing. Just because Entercom is now Audacy doesn't mean they're going to make expert decisions. It doesn't mean they're going to make more money next year than they did last year. Experts probably know this. The 401K holder is more or less clueless about it.
If your company is listed on either of the stock exchanges, or openly sell shares, you're regulated by the SEC among others. That means filing some of your financial and tax reports publicly. Those financial reports include certain guidance on the financial health of your company, and to an extent, forward looking plans.