You have full control over what is shown. In fact if you click on any individual trophy, the option to delete is shown. It's easy enough to move trophies in and out of your showcase though. The other option is to "feature in showroom", click around a little bit, you'll figure it out. I think the last of the eight featured goes into "storage" when you "feature" a new trophy, but it might be the first.
Reset trophy showcase. Is it possible?

Thanks baddogno. Actually I want to feature no trophies at all, I mean, when you join chess.com, as you gain trophies they are automatically shown in acquirement order, without the need of a feature tool.
I want to reset (in fact, delete the custom order of) all my featured trophies so the showcase could regain that natural flow that is standard, which is to show the last 8 trophies won, most recent first and eighth last.

I mean, just like your trophies are shown, see?
Without my human finger choosing trophies to feature, but, instead, showing the newer first, as it is standard here.
But I don't see an undo option to make that happen again.
(I say undo option because you can feature trophies, but once you did it there's no turning back to the natural flow, I guess...)
It's been a while since I administrate the trophies that will be shown at my trophy showcase, but I got a bit sick of it. I want the natural flow to be reinstated, however, I don't know if it is possible by means of settings.
If it isn't possible, I turn this a suggestion for the proggy fellas of the website, so one can easily undo a thing that he desires to see no more.