Not sure on the ID I'm afraid. Just wanted to add a note that most of the folks here don't find the 'Just add ice' watering method works for them.
It may work in some enviroments, but in general phals like luke warm water and cold water is not so good for them. Also it's generally recomended to water thoroughly with water running through the pot, make sure it's fully drained (holes in the bottom of the pot is a MUST) before putting it back in the coloured outer pot (I think I can see an inner and outer pot in your third pic). Wait until the medium is dry all the way through (the roots are silvery right to the bottom) then do the same again.
I should add that some folks have had success with the ice method, but it's not generally advised.
I'm not sure on the ID, but Phal amabilis is a large white phal. However there are a lot of hybrids that also are large and white (often with a large influence from amabilis).
Sometimes growers who don't care that much about names (mass market growers) will use a name which is just one parent in a hybrid. I've seen phals sold as gigantea when they looked more like a very large amabilis.
I have no idea if 'Just add ice' is the same, and whether what they sell is actually amabilis or just a name they put against them as the predominant parent.
I had no intentions to water with the just adding ice method. She's been watered once with lukewarm water since I got her. She was dried out and the blooms were droopy, but as you can tell, they perked up and didn't drop!
There is a plastic inner pot. I was so happy to see that! Meant I didn't have to figure out how to repot with my first one to get it out of the possibly "toxic" decorative pot.
One thing you should do is make sure the inner pot has some holes other than a bottom one for drainage and air circulation. Also they often come packed tightly in sphagnum moss and the roots can rot quite quickly like this. If it is like that, maybe you can lift the whole thing out of the pot and inspect it, and possibly pull away some of the moss to have a looser airier arrangement till it is done blooming. Then you might want to re-pot in something such as bark.
there are several holes in the bottom of the plastic pot - i think 4, if I remember right.
I pulled the plant out of the plastic pot to inspect the roots and all, because it looked like there was green stuff growing between the media and the plastic. It doesn't wipe out so I don't know what it is/was. The media does seem like it is bark and is starting to decompose, so I think I'll have to repot pretty soon to replace the media.