Does anyone know the name of this specific part?
It's a generic linear taper slide potentiometer. You probably won't find a specific manufacturer or part number, unless you can match the 1630 to something. Instead you'll have to search for datasheets to find one of matching size.

The number B10K means B-taper 10kOhm, where B-taper indicates that the resistance changes linearly as you slide it. This is as opposed to logarithmic or audio tapers.