Neil Simon had a lot of his best work ahead of him when the Alvin was renamed in 1983.
Ethel Barrymore while quite dead these days, was also at the top of her game when the theatre bearing her name was built in about 1927.
Belasco named his theatre for himself. When Billy Rose owned what is now the Nederlander, it was called the Billy Rose. Ziegfeld built the Ziegfeld at 54th and 6th.
The Broadhurst was named for a then-popular playwright who was still working when it was built.
The first Helen Hayes Theatre on 46th St. was renamed for her (1957?) when her career was winding down, but she was still working onstage and did so occasionally until 1970.
The Lunts last play, The Visit, was the first attraction to play the Lunt-Fontanne. They were not young, but they did this play for well over a year total first in New York, then on tour and then I think London.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher