Is there a term to define the influence and sharing of common expressions among people? I'm wondering how to call the phenomenon that happens when people spend a lot of time together and end up sharing similar vocabulary or reusing the other's expressions? Is there a term for this?
You might be referring to mimicry or linguistic mimicry. Mimicry is more broad than just vocabulary and expressions, but the general principle of imitating what others in a social group are doing applies.