I wonder how many such monumental "brand name" physicists are still alive.

We still have Witten, Weinberg, 't Hooft, Yang&Lee. Also Nobelists but (in my utterly prejudiced view) less monumental: Rubbia, Glashow, Wilczek, Thorne. Not Nobelists but arguably in the monumental category: Dyson, maybe Penrose.

For "brand recognition" surely Peter Higgs is at the top, along with maybe Dyson. I'm not qualified to opine on how his work compares to the others.

I don't think Higgs is really widely considered monumental in the same was as those other people. He had one good idea (at essentially the same time as Brout, Englert, Kibble, ...) which got his name attached. But I am a professional physicist and know none of his other work, in contrast to Dyson, Weinberg, Witten, t' Hooft, ...

Higgs is absolutely a more familiar name than the others, and stain too, whether you think his contributions were proportional to that recognition or not

That he has greater name recognition amongst lay people doesn't make him a monumental physicist.

PW Anderson (Nobel Laureate, 95 yrs old) Condensed Matter Physics legend

Schrodinger's cat, maybe.

Nope. I checked.

Maybe Susskind. I'm not sure what definition of "monumental" we're going with, but he's surely "brand name."

Maldacena seems like a good consideration. Maybe Alan Guth.