Gerry Schoenfeld refuses to rename any of the Shubert houses. This rules out the Majestic, Plymouth, Royale, Imperial, Longacre, Broadway and Ambassador. The Winter Garden, Lyceum and Music Box have too historically ingrained names as does the Nederlander-owned Palace to change them.
But certainly someone could rename the Minskoff (named after the developer and theatre investor who put up the building it is in), the Marquis (named for the ugly hotel in which it resides), Circle in the Square (a bankrupt entity), St. James, Studio 54 (a disco for God's sake), even the Biltmore.
Not only Sondheim but Ethel Merman, Mary Martin, Cole Porter, Julie Harris and Colleen and Jason could have theatres named for them.
I call the American Airlines Theatre by its given name, the Selwyn, and I still call the Neil Simon the Alvin. I can't break the habit with the latter.
RIP: the George Abbott, Morosco (the best theatre in NY), the first Helen Hayes, Bijou, the original Ziegfeld, and Playhouse all of which bit the dust in my lifetime. And the Hudson and Henry Miller's too.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher