I agree with those before me who have mentioned Ethel Merman. She was known in her day as the First Lady of the American Musical Theatre, just as Helen Hayes was known as the First Lady of the American Theatre in her day. Miss Hayes had a theatre named after her on 46th Street which was torn down in the 1980's to make way for the Marriott Hotel. Then they named the Little Theatre on 44th Street after her.
They could re-name the Imperial Theatre on 45th Street after Ethel Merman since she had some of her biggest hits there: ANNIE GET YOUR GUN, CALL ME MADAM, and GYPSY (which transferred from the Broadway late in its run).
Brooks Atkinson was the very highly regarded theatre critic for the New York Times for decades and that is why he has a theatre named for him. Walter Kerr similarly was a highly regarded, fair theatre critic, first for The New York Herald Tribune and then, when that folded, for The New York Times. Thus, Kerr has a theatre named for him.
"Madam Rose...and her daughter...Gypsy!"