Mike, I don't think that developers hire signature design firms so that they get to hang out with the signature, but because they think the name will help them sell houses/attract people to their resort/whatever. It's a business decision not an ego one.
So the survival of the Palmer design firm in the future fundamentally depends, as David and Tom have been discussing, on whether that brand name continues to have value, so the firm can continue to win business (and, for that matter, attract and retain architectural talent: if Thad and Brandon, and anyone who might follow them, conclude that they'd do better operating under their own names then bang goes Palmer).
Will that be so? It's hard to tell, though I have had extensive discussions with messrs Johnson and Layton on the subject. Their view is that, as the stewards of the Palmer brand, they have over 300 courses that will continue to need architectural support in the future for whom they are the natural, go-to partner, and that this gives them a strong base from which to pursue other business. As to that other business, it will in the end come down to whether the two of them do good enough work and are sufficiently convincing in a sales environment, to attract new clients.
As David mentions above, it's perfectly normal in other professional services sectors for businesses named after the founder(s) to survive and prosper post those founders. That has not been so in golf course design up to press, except in the case of firms that have been run by multiple generations of the same family (Maples, Hawtree, Swan, Harradine, Jones to an extent to name a few). But golf design is a small industry with only relatively few practitioners, and it's dangerous to draw firm conclusions from a small sample. It is an interesting topic. But in the end only time will tell.