So...I have seen that "σύνθημα" has been translated as "password" and as "cue." To me, those are not very related meanings...a "password" is a particular word that one must know in order to gain access to a program, website, club, etc. and a "cue" is either a reminder that one gives to an actor or presenter who has forgotten what he/she was going to say or a certain sound or other prompt that calls someone into action (e.g. "There's the bell- that's my cue- I gotta go now.") So...σύνθημα covers both of these meanings?
Actually σύνθημα does mean 'cue', but I don't see how it could work in this example in English.
Note that you'd never say 'that's my cue' in Greek, unless it is the cue that you have created and suggesting to be used! Examples of standard use are "Αυτό είναι το σύνθημα (π.χ. για να φύγω)", "Δώσε το σύνθημα".
Σύνθημα is also a short phrase that fans would shout during a sports game either to support their team or to mock their opponents.
Password is most often translated as κωδικός πρόσβασης (access code) for any kind of lock, but it would also (or even primarily) be σύνθημα if you're knocking on a door and you have to say it to be allowed through.