They can remain “one of the leading firms in XYZ” forever, at least as far as anything goes that is recorded anywhere.
And I would be careful about verbally saying their name too.
What you do for your first client when trying to sign up more clients, will speak volumes to those additional prospective clients for how you will treat their names and data once they sign up.
So, don’t ever give away the name of that first client. And don’t ever give away the names of any other clients who also request anonymity. After all, who wants to sign up for white label service from a company who blabs about who their clients are?