The Qunari/Kossith have no name for their people. Qunari/Kossith is/was used to define their race. Without it they simply call themselves "Vashoth" or "gray ones". Those who believe the Qun is detrimental to their people call themselves "Tal Vashoth" or "true grey ones" as they feel that being free of the Qun is the proper path for their people.
That's what i've gathered from reading through this thread.
Sounds about right. People keep saying that "vashoth" is the name for racial qunari born outside the Qun and this really seems to contradict what the devs have been saying so I was a bit confused about it.
Those of the qunari race must be seen by the Qunari as part of Qunari culture even if they were never actually part of the Qun so they are considered Vashoth and not Bas.