Is it so informal to answer "очень приятно" with "познакомиться" ?
These phrases do not answer each other. When somebody is introduced or introducing themselves to you, you can answer:
Очень рад! (typical of men, I've never heard a lady to answer "Очень рада!" when sb is introduced to her)
It all has the same degree of formality, as you are saying it to an unknown person. Less formal will be not to say that at all, but you should be attentive to the society you are in to make sure it is concidered polite there and what people say instead. E.g., it can be "здорово, а я ... (the name)".