There are over 300 universities in Korea and many of their names are shortened in spoken Korean, not necessarily because they are too long, but because it's more convenient and quicker to use the shortened names. There is no fixed rule as to why certain university names are never shortened. In this video, teacher 경은 (Kyeong-eun) introduces 15 of the most commonly used shortened university names in Korea. 

You can check out the entire list in text format at http://TalkToMeInKorean.com