Agreed. I think it's likely that "Eagles" will continue as a brand, even if no-one plays under that name. We know there are plans for a musical and I expect Azoff will continue to look for ways to exploit the name and back catalogue (and Henley will probably resist).
From various books, interviews etc, I believe that the name became the property of Eagles Ltd in the 70s to remove the risk of ex-members touring under the name as had happened with The Byrds. When Bernie and Randy left, they gave up their claim to the name, along with their shares leaving the name effectively owned equally by Frey, Henley and Felder. Of course, we don't know if there were changes as a result of the settlement of Felder's lawsuits or what happens to the shares in Eagles Ltd when a shareholder dies. It's possible that Felder has as much claim to the name as Henley.
However, even if Felder has a claim to the name, I don't see much advantage in him exercising it. There's little doubt that Azoff and Henley would object and that would be costly. Besides, the brand would probably earn more for him if left in Azoff's management.