This is TYPE-MOON, does Melty Blood or Fate/Stay Night make sense to you either?
Yes in fact, they do. They make complete and perfect sense to me.
You see, the name Melty Blood is actually referring to the game's Heat Gauge. This gauge is so awesome you see that it can in fact reach a temperature so high that it can cause blood to melt and become... melty, yeah. Thus the name Melty Blood.
As for for Fate/stay night
(with 'stay night' having no capitalized letters in it, you should know this) it is obviously referring to something far more DEEP. For this, let's have a closer look at the Fate route segment entitled stay night; here is where Saber leaves, obviously this is the 'Fate' that the name refers to - how she and Shirou must be separated, because it's fate. Or something. But of course Fate would refer to her she is Fate's poster girl, it only makes sense that the series' title refers to her.
As for the stay night part, it is clearly referring to how it is their last night together and for them to remain so it would involve that night becoming never ending or something... yeah. But it is not to be, because it goes against fate... or something.
It's all very DEEP but it makes sense... I think?
It should go without saying, but obviously I just made all that up just now.