According to Ovid, the fruit of this plant got its characteristic shade of red from the blood of Pyramus, who had killed himself upon suspecting that his love, Thisbe, had been eaten by a lion.
A 1986 song which includes a street with this name also titles an episode of Moonlighting which included a famous dance number to the song, and opens with these lyrics:
Why can't I lay low
Why can't I say what I mean
Why don't I stay home
And get myself into some boring routine
(Big Man on) Mulberry (Street)