iTerm.app

Hit Cmd-I, set the Title, hit return, then click the "Update Default"
button. Then create a new window with Cmd-N. The Window still has the
title "Default" and not the new title that was just given.

(If the ONLY way to get a new title to stick is to create a new profile of
some kind, that seems like a lot of work, particularly when one is happy
with the settings as they are.)

An additional annoyance, if you hit Cmd-I and set the title by typing into
it, then close the window without hitting return, the setting does not
take. This is unlike other OS X applications (Terminal for example).