Glaceon, as an Eevee is Yui's third Pokemon she caught in Full Moon's Full Pokemon Journey.
In a future episode, Yui's Eevee is set to evolve in the second season, she was caught prior to The Light Music Pactio Club!. After Yui made a pactio with Negi, she joined Yui to be her traveling pet companion.
In "What's In a Nickname?", she was officially nicknamed Glaciar by Yui, and even nicknamed the other Pokemon she has.