" Then he dropped into conversation that Janey was the sister of Miriam Pendergast, with whom we d gone to high school."
d_r_siva
drop into - Pass quickly and easily into (a habitual state or manner)
https://en.oxforddictionaries.com/definition/drop_into
busterwasmycat
drop in means to just put into the conversation but with no real reason (it is not important to the rest of the conversation). Fits with the same idea as name-dropper (someone who finds a way to always mention the names of important people they know even when those people have nothing to do with the conversation).
drop in means insert (put in), but gives it the idea of accidental insertion whereas put in gives the idea of it having been done on purpose.
Cara
It means that he happened to mention this fact, while a conversation about something else was going on.
Anonymous
The meaning is that the "he" concerned name-dropped a well known celebrity, as is the wont of someone given to bragging about his many female conquests. His intention was not merely to give incidental information, but to enhance his own self-importance. The wording "he dropped into conversation" is perfectly idiomatic.
yet-knish!
Not grammatical. It would have to be "dropped into THE conversation".