"What is the origin of our name?"
Translation:Qual è l'origine del nostro nome?
It is not.
You may use "qual è" when the choice is between two or more issues, either definite (which) or indefinite (what):
Qual è la tua canzone preferita = What is you favourite song?
You may use "cos'è" when you want a definition of some thing:
Cos'è un atomo? = What is an atom?
In this particular case, you don't want a definition of the "origin of our name", you want to know the origin among all the possible origins. If the question was "What's the meaning of our name?" the italian would be "Qual è il significato del nostro nome?". But if the question was "What does our name mean?" then it would be "cosa significa il nostro nome?".
In the first case you want to know what the meaning is, and the answer is: "the meaning of our name is ...." In the second case you want a straight definition of the meaning, and the answer is "Our name means ...".
So, in the first case you give a particular meaning among all the possible meanings, in the second case you don't.