What is the point of naming anyway? 
  
In my point of view it is to distinguish between peaks. For instance giving Sherman Pk a separate name from Baker. 
  
If you don't climb separating out the different peaks and naming them individually is not so important. The Chilliwack natives called the whole Border Peaks area "Putlushgohap" or "Tomyhoi" according to good ol' Henry Custer whose adventures I am now devouring (thanks Harry!). Now we have five separate peak names in there, ABP, CBP, Larrabee, Pleiades and Tomyhoi itself. (And Petlushkwohap is up near sKihist in the Fraser Canyon  ) 
  
So basically my view is that it's OK to name anything with a distinct route to the summit. No matter how much "prominence" or other arbitrary criteria, the summit has. 
  
As for new names: what are the most overused mountain names? Around here there are TOO MANY Red, Green, Goat, Bear, Needle, and Cathedral peaks. NO MORE!