Magma can indeed contain crystals since not all crystals form at the same temperature. That being said recovering and actually dating those crystals is beyond current technology. But in generally it is not impossible just difficult.
I have on idea if it has a separate name since most magma would have it. That being said diffusion would be a huge problem so you could only date young magma or see which crystals are least affect. But hey its a moot point unless you can go sample a piece of magma.
Actually if you look at Zircons with uranium lead the lead would move a few nanometers in millions of years at 900C or so. In that case you do get a solidification age. Diffusion can be a problem but not in all cases.