Important data on the First Order’s Starkiller Base was revealed on November 15, 2016:
“Starkiller Base was once a little-known planet rich in energy-focusing kyber crystals, some of which were used for the Death Stars’ superlasers.”This description matches well with the secretive Jedi planet Ilum, a planet rich in energy-focusing kyber crystals that the Jedi mined for their lightsabers. The Empire also heavily mined Ilum for its kyber crystals, going so far as to expose its core.
Thus, if the Ilum kyber crystals went into the Death Stars, then this would seem to identify this mysterious Starkiller Base planet as Ilum.
See also: https://youtu.be/ozd5kwz4cjM