Container of two halves, name seen in mine with lid flipped (4,3)

'container of two halves' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'name seen in mine with lid flipped' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'seen in' is an insertion indicator.
'mine with' becomes 'pit' (as in a mining pit. I am not sure about the 'with' bit.).
'lid' becomes 'top' (eg a bottle top).
'flipped' is a reversal indicator.
'top' reversed gives 'pot'.
'n' placed into 'pit' is 'pint'.
'pint'+'pot'='PINT-POT'

Can you help me to learn more?