The Day Lady Died (title)
The title leads us to believe the poem will be about the death of "Lady," or Billie Holiday. But most of the poem is just a narration of the "day," as in, the completely normal things the narrator has done. In that regard, the poem isn't technically misleading, but it tricks us nonetheless. It would be like giving a poem the title of "My Breakfast on the Morning of 9-11" and then preceding to write about your breakfast cereal. Awkward. Obviously there's something else going on here, but we'll leave it to you to figure out why O'Hara makes this interesting choice.
I go on to the bank and Miss Stillwagon (first name Linda I once heard) doesn't even look up my balance for once in her life (lines 11-13)
In these lines, the speaker suggests that this day is somehow "different" from other days. Maybe Miss Stillwagon doesn't look up the balance because she is so grief-stricken about Billie Holiday. Or maybe it's just a total coincidence.
and a NEW YORK POST with her face on it (line 25)
This poem is an elegy, but the speaker never refers to the deceased person by name. Billie Holiday is just simply "her."