Pik Lenin has like many of the other Soviet era peaks officially been renamed. The problem in this case is; it has gotten many new names.
Some says Peak Kaufman is the new official name. It was also the original name before it was called Pik Lenin.
The Kyrgyz authorities claims the new name is Pik Sary Tash and the Tajik president's official site declares the official name is Abu Ali ibni Sino (Avicenna).
The problem is none of the names have won acceptance and I have heard NO one using any other name than Pik Lenin.
Yes, it's the Kyrgyz side and what you see below the mountain is a settlement. It's a semi-permanent one, consisting of some yurts, BC tents and also some normal mountaineer's tent. The place serves as an ABC and is about 1h walk from BC.