Actually, they do have names. In ME2 Legion says Sovereign (the name made up by Saren) referred to itself by name as Nazara. One assumes that is the name of the race that was used in it's creation.
That would still be a name given to it by others; either by the Nazara themselves, or by Legion when he realized that Sovereign was created from
the Nazara. Or, more likely, whoever Sovereign had been talking to before he spoke to Legion.
Harbinger is an odd one since, being an english word you'd think it was another made up label, but the reaper you kill on Rannoch says to Shepard [I]"Harbinger speaks of you."
That's kind of what I mean. "Harbinger" was mainly a title he used while controlling the Collectors and threatening everyone. It's more of a descriptor than a name. When you consider that the Reapers' primary mode of communication probably isn't linguistic in the first place, the only reason they would even NEED names is when speaking to organics and some times the Geth, in which case they are content to use whatever random labels organics have slapped on them.
If Harbinger had first been encountered by the Volus, for example, the reaper on Rannoch probably would have said "That Horrible Thing That Killed Everyone
speaks of you."
Perhaps it's real name directly translates as "Harbinger"?
More likely, it isn't a proper noun so much as what Harbinger literally
is. It's like if you had a crewmember on your ship whose name just happened to be "Stupendous Badass."
OTOH, it's worth considering that "Harbinger" might actually refer to the Reapers themselves; a translation, for example of a word used by one of the races that predated the Protheans, referring to the Reapers as "The Harbingers."