Who Deserves a Broadway House Named After Them?

Annaleigh Ashford.

No, but for real, "The Fanny Brice Theatre" sounds grand. I'd also love "The Irving Berlin Theatre", among others.

I feel like if Rodgers got one then so should Hammerstein, especially since he was the one more directly involved in reshaping how a musical could be structured.

I definitely think in terms of playwrights, Albee and Williams are at the top of the list.

Composer wise I would also agree with Irving Berlin.

Perhaps even Julie Harris as well.

Arthur Miller

Miller directed that only one theater -- at his alma mater, University of Michigan -- is to bear his name, so there won't ever be an Arthur Miller Theatre on Broadway.

The Dennis Quaid Theater for Performance Art

The Jan Maxwell Theater (where every show is guaranteed to lose at the Tony Awards)

The Davenport Theater with Tweet Seats

While, I agree with some of the ideas, I like all the names on the current Broadway houses. BUT, I don't want some of the famous theatres to get renamed (St. James, Majestic, Palace, Winter Garden). Some of those names are just has deserving as some of those included.

The question also is, why does every theatre need to be named for someone?

The Apple Merman Theater

The Microsoft Comden-Green Theater

The Audra McDonalds Theater

Andrew Lloyd-Webber doesn't deserve a theater named after him.  He's rich enough to buy his own like he's done in London.

The Bob Fosse

The Michael Bennett

The Chita Rivera

The Jerry Herman

The Garland/Minnelli (see what i did there??!?)

Stephen Schwartz and Oscar Hammerstein

The Stritch.

"The Stritch."

 HAHA. Yes. 

Also, correct me if I'm wrong, but wasn't the Music Box once named the Irving Berlin Theatre?

No one has said Mary Martin. 

What about Jerome Kern? Absolutely a major influence along with Hammerstein in developing the modern integrated musical  

George Abbott

Agree, sort of, with Irving Berlin but I automatically think of him with the Music Box. 

Cole Porter

""The Stritch."
 HAHA. Yes. 
Also, correct me if I'm wrong, but wasn't the Music Box once named the Irving Berlin Theatre?"

 It has always been called the Music Box Theatre, but it was constructed by Berlin to house his "Music Box Revues," so some may have called it Berlin's Music Box, especially early in its history when his association with it was still standard knowledge.  It was co-owned by his estate and the Shuberts until fairly recently, like in the last five or ten years, when the Shuberts took full control of it.