The forsaken (or undead) are dead elves and (in most cases, including playable characters) humans who had been brought back to life by the Lich King. They have since broken away, and are now led by an undead high-elf, Sylvanas Windrunner. Because they're essentially humans and elves, they also have human and elvish names as the forsaken.
The forsaken usually keep the names they had when they were alive, so their names will often be human. However, many forsaken simply don't remember the name they had when they were alive, and instead choose a new name. Many forsaken mistakenly think a nearby tombstone has their name on it, for example.
It's also quite common for a forsaken individual to take a name from one of their possessions, as they think they belong to them, even if they stole or borrowed them before they died.
A fallen soldier may have had a letter from a fallen comrade meant to be send to that comrade's wife. Instead, the forsaken individual may think they wrote that letter, so the name at the bottom logically belongs to them.
Last names are usually taken in 2 different ways. Either they choose to hold on to their human roots and memories, and choose to stick with a human last name in the same fashion they 'choose' their first name.
Alternatively, they choose to fully embrace their forsaken fate, and pick a new last name to accentuate this. Names such as Blightbeared, Deathrunner, and Lostweeper.