How does something get its name?

Blue items can have up to two affixes. Many of these have an associated modification that will be made to the item's name. Some affixes prefix the item's name with something, and others suffix the name. This, in fact, is how they came to be known as "affixes" in the first place. This is a holdover from the original Diablo and Diablo 2, where it worked similarly.

Here's a database of all the affixes.

For example, if you go to "Regen" (which is life per second), you notice that on an amulet or ring, depending on the level of the item, it will be a "Reptilian", "Salubrious", "Undying", or "Immortal" item. If you look at "Maximum Damage" for amulets/rings, you'll notice that it can be "of Wounding", "of Agony", "of Malice", etc., depending on the item's level again.

Taking this together, if you get a "Salubrious Amulet", you'll know it gives life per second. An "Amulet of Malice" will give you maximum damage. A "Salubrious Amulet of Malice" will give both.

Rare items also use these same affixes, but they don't affect the name of the item in the same way. I do think that the item affixes influence the name on rare items, but I don't think it's well-understood how exactly that works.