
To be fair, "Reapers, a label created by the Protheans to give identity to their destruction." Sovereign said that (or something along those lines). You've got a race of giant space monsters that appear to be harvesting your civilization...kinda like you're a bunch of crops being reaped for the harvest.
That is, the Reapers don't really give a fuck what you call them, they're gonna do what they're gonna do. Calling them "Reapers" is just attaching a name to them because that's what they're doing: reaping. So it's not so much "We were named Reapers so we's gonna go out raping REAP! Reaping!" but rather a case of "These giant monsters appear to be harvesting us, so lets call them Reapers."
The action came before the name rather than the name determining their actions.