Ok, so assume a business is generating a lot of money from online leads, search engine results that drive customers to that business with cash in hand.

Assume that the business owner wants to sell the business.

Assume that the business name must be changed for legal reasons (this is a law firm, and the name has to be changed when the law firm changes hands).

The name change will destroy all the search engine rankings that have been built up over time.

So how does one go about selling such a business while preserving its main source of revenue, that which makes it worth buying?

basically you keep the old url that all the traffic went to, then depending on how you want to handle the redirect, you can either replace the main page with some letter explaining, so and so law firm has been purchased by this and that law firm.
please click on the link to be directed to this and that law firm web page.

or you do an automatic redirect to the new url for the new named lawfirm.

Either works, but both will alienate some of your clientel.
The first is the most transparent and explains what happened. The second can get people bent out of shape because they thought they were going somewhere else.

Eitherway till the this and that firm gets established, they would have to own both domains.

Why would the firm name change?  If it is Katz and Teller, just keep the name.

This. Nearly no one buys an actual business entity because of liability. They buy the assets and form a new company.

Example, the last company we bought was "_________ Auto, Inc." We bought the assets and operated the new entity under "_______ Auto, LLC."

The sign didn't change, still says ______ Auto. We sent a letter to all of the customers explaining it bc my brother had worked for that company for 14 years previously and we were proud of that fact. Apprentice turned tech turned manager at a dealership, turned owner of the first place he worked.