"just was wondering if the point in the PH diagram had a name"
if it follows the definition for cricondentherm I would call it cricondentherm in all diagrams (in the same way of other critical points),
however, as for other critical points, PT diagram seems to me more immediate to interpret (visually).
About your problem (verify if there is intermediate condensation for a mixture along some line with a specified value for H) of course you may solve with a series of flash operations, may be you are looking for a more efficient option but in my opinion that could require some intermediate steps for a mixture...