I do. In the index of the second link the whole Karakoram Conference report has been given. If you go through the notes you'll realize that where a local name of any mountain, pass or valley was present it was always adopted. If there wasn't then a name was derived from the most major adjacent feature which did have a local name. The only exceptions to this were K2, Broad Peak and the Muztagh Tower (although Muztagh Tower is clearly heavily influenced from the local language except for the word "tower"). This was mainly because these three peaks did not have any local names.
K2's naming is actually very interesting. Until K2's discovery by the westerners few people, including the locals, knew of its existence, the same went for the Gasherbrums and Broad Peak as well. Nobody in their right mind ever wanted to walk across the Baltoro Glacier (local cultures had myths that beyond the snout of the Baltoro lay the place where demons lived, others thought it was where fairies lived and then add a hundred more myths). You might think that you could see K2 and her sister peaks from other mountains closer to the inhabited valleys but you'd be wrong. These mountains are completely curtained off from the rest of the world by other seriously tall mountains all around them. It was only in 2010 that a place (Iqbal point or the vertical point) was discovered North-East of the Hushe valley from where you can actually see K2 in any appreciable way on very clear days, but you have to climb 6000 meters to get there (!!!). Basically no one knew that these mountains were actually there (imagine that!). Due to this these mountains had practically no mention or significance in the local cultures and thus remained unnamed.
In the 1950s, under the Great Trigonometric Survey, Thomas Montgomerie was sent to mark out the most prominent features of the now Northern Pakistan. While on Mount Harmukh (in Indian occupied Kashmir) he observed two very tall and prominent peaks far off in the distance. He drew a sketch of the peaks and for record keeping designated the seemingly taller (only because it was closer) one K1 and the second K2, where the 'K' stood for the Karakoram and the '1' and '2' stood for a numerical designation. This is that sketch:
The designation for K1 held for a little but soon gave way to its actual name; Masherbrum. Masherbrum was/is a very well known and observable mountain for the locals and thus had a name. The second unknown peak, however, did not and so the designation 'K2' stuck around. Numerous attempts have been made to give it a name in one of the local languages ('Chogori' is one of them) but none have stuck (the locals themselves call the beauty K2). Some narcissistic white men tried their best at getting it named Mt. Godwin Austin but that failed too.
My opinion on this matter was shaped by a low level mountaineer's blog who's name I can't remember. I'll paraphrase. In his opinion the designation K2 perfectly defines the very nature of the mountain i.e. the name K2 is perfect exactly because it is not a name and just a designation. Giving K2 a name will be an attempt at humanizing it when it is the epitome of inhuman and beyond human. It's character is savage, wrathful, unforgiving, terrifying, and most importantly unaccepting of the so-called might of the human spirit, will and arrogance, a character which cannot be explained let alone summarized in a human name. And thus any human-given-name will be disrespectful and arrogant.
I can't agree more.
If you notice it, the 'persona' or the 'ring' that the word "K2" gives off can't, at least for me, even be described in sentences.
True, however, the rate of melting in the past few decades has far exceeded anything that we have ever seen in the planet's history. I'm talking about millions of years as observed through scientific means. The retreats which have occurred in a few years used to happen over hundreds of years. I for one am not willing to take any chances.