I've never heard anyone say double block diamond, only ceiling double diamond or roof double diamond.
Ya, you're right, ceiling double diamond is what people usually call it.
A double invert is pointless because it's just literally 2 inverts in a row.
I see what you're saying, but I think the jump is common enough that its existence should be acknowledged. Like, there isn't one universally accepted form for a double corner, but the double invert is a specific and rather common position (well, in needle games, probably not in the games most people play, though many people would probably be curious about the hardest common positions anyway) that comes up relatively often in discussion.
Your triple diamond is meh because there are a lot of possible heights
Ok, then erase the 40 px. The point of that was to emphasize that, in its most common form, the triple diamond is raised a little, though I suppose that's clear from the positioning of the block in the image. The triple diamond isn't necessarily a common position anyway, though since the diamond and double diamond are included, not including the triple diamond suggests that it is impossible or never used.
(in contrast to the 16px gap you can actually see that it's 4.5 blocks without having any knowledge in pixels).
Good point. I mentioned the 4.5 block jump because 16 px gap was included, but yeah, there's a clear difference in how much prior knowledge is required to understand the terminology.