What is the proper term for lines of constant volume and constant enthalpy on a thermodynamic diagram? I know an isotherm is a line of constant temperature.
Isobar is a constant pressure line.
Isentrope is a line of constant entropy.

But what do you call a line of constant volume? An Isochore?
And what do you call a line of constant enthalpy? An "isenthalp"?
But what do you call a line of constant volume? An Isochore?


Correct.


  And what do you call a line of constant enthalpy?


The process is isenthalpic. More than one engineering/thermodynamic text I found by Googling indicates they are simply referred to as "isenthalpic lines." See this for example.