Poets named for hospitals is a very short list.
In fact, Edna St. Vincent Millay is probably the only major poet who would be on such a list. Frankly, I can't think of anyone else named for a hospital, let alone a poet, and if you know of one, please let us all know in a comment.
Edna's uncle's life was saved by the staff of St. Vincent Hospital shortly before Edna's birth in Rockland, Maine -- consequently, Edna's middle name. Somehow this still seems odd. What if her uncle had been saved at Mt. Sinai? Columbia-Presbyterian?
Appropriately, Edna, or Vincent, as she liked to be called, came into her own in the Village, living in the famous narrowest house of the city at 75 1/2 Bedford Street, about a three minute walk from Hudson Park. She won the Pulitzer Prize for Poetry in 1923, the first woman to do so.
Hudson Park is currently hosting a display about the life of Vincent in its Reference Room Gallery. April, aka National Poetry Month, is a great time to check it out!