From reading the prequel book "Before the Awakening", which deals extensively with Finn's training and run-up to Jakku battle:

1. The name of his training location(s) is never mentioned

2. However ([as detailed in my other answer on the site, with proof][1] - or [another, same-themed answer](http://scifi.stackexchange.com/questions/111305/why-was-finn-on-jakku/113346#113346)), **at least a part** of his training was on the Starkiller world, in the infamous "sanitation" scenario 

   The only 3 things he did AFTER his training finished was:

    - Embark on a ship to travel to his first post-training assignment (Pressy's Tumble mining center on an asteroid in Pressylla system)

    - Bungle up that assignment by failing to shoot at unarmed civilians

    - Get swept up with everyone else there by Captain Phasma, to go meet Kylo Ren and depart for Jakku

    This means that, whenever he did his "sanitation" work on Starkiller, it was before his training ended.

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For completeness, in New Disney Canon, Imperial training was on Arkanis.

Visual Dictionary page for General Hux says that his father was a "highly placed official in the Imperial Academy... on Arkanis" (later in the same page it said the father was the "Academy commandant")

  [1]: http://scifi.stackexchange.com/questions/113301/why-was-fn-2187-working-in-sanitation/113304#113304