What is this dough called?
First, I wouldn't call it a roux. There is a difference in flour gelation when the flour is presoaked in fat (as in roux) and directly mixed with water (as in pate a choux). The butter in pate a choux doesn't coat the flour first the way it does for a roux. Plus, a roux is prepared with way more liquid. 

As for a proper name of this kind of dough, I don't think there is one - for the simple reason that nobody has a proper use for it. I mean, you don't give a name to every stage of the mixture when preparing a batter, so why should you do it for pate a choux? 

This is what McGee has to say on pate a choux. Note that the eggs are important for both texture (the "richness of yolks" smooths it, probably more due to the lecithine than the fat) and structure (egg whites trap the air pockets). So why should anybody ever make it without the eggs? And if it isn't used as anything but a prestage of pate a choux, why give it a name? 



As for the uses of pate a choux, Ruhlman gives a fairly comprehensive list in Ratio. It mentions  


cream puffs/éclairs 
profiteroles 
gougéres 
parisienne gnocchi 
pets de nonne, beignets 
churros, funnel cake 
panade for pâtés 
pommes dauphine 
binder for potato pancakes 
Gnocchi à la Romaine (made with durum semolina)
"There's no end to what you can do with this stuff."