In book 5 the Gryffindor password is mimbulus mimbletonia, the plant which Neville has just been given for his birthday.
"Harry, I know it!" Someone panted up behind him and he turned to see Neville jogging towards him. "Guess what it is? I'm actually going to be able to remember it for once-" He waved the stunted little cactus he had shown them on the train. "Mimbulus mimbletonia!"
(Order of the Phoenix, Chapter 11, The Sorting Hat's New Song)
The passwords are picked by the Fat Lady, as Sir Cadogan chose his own assortment of passwords when he was standing in for her. Yet mimbulus mimbletonia is a very rare plant, apparently only to be found in the Middle East.
"It's really, really rare," said Neville, beaming. "I don't know if there's one in the greenhouse at Hogwarts, even. I can't wait to show it to Professor Sprout. My Great Uncle Algie got it for me in Assyria."
(Order of the Phoenix, Chapter 10, Luna Lovegood)
It seems strange that the Fat Lady would pick a plant that Neville happened to have acquired over the summer as the new password.
Is there an in-universe reason for this or is it just a coincidence?