Google Translate says 上海外国语大学 means Shanghai International Studies University. Shouldn't it mean Shanghai Foreign Languages University?
The official site of 上海外国语大学 has its English name as “Shanghai International Studies University”
Translation of proper names does not always follow normal translation rules.
Apparently, now the department, schools, etc. specialized in foreign language teaching are translated by International Studies. For instance, the Zhejiang University's school specialized in foreign language teaching is named School of International Studies. It might be related to the fact that not only foreign languages per se are taught, but also foreign literature, politics, etc.
Google translate is not wrong in translation.
It just goes for general translation rather than proper nouns (as @fefe mentioned).
And this is always not a simple translation when something comes to historical.
From 上海外国语大学-wiki, you'll see the chinese name was given in 1956 exactly for "learning foreign language" only, but it expanded the scope of education in 1980s.
Apparently, there was no English name officially given until 1985, check second paragraph "历史承传" on SISU website.
1985年经教育部批准，学校英文校名确定为“Shanghai International Studies University”（缩写为“SISU”），并于1994年正式更名为“上海外国语大学”。
In general, Chinese universities tend to keep the chinese name so as to preserve the history behind (if you could understand the paragraph title mentioned before, "历史承传").
While the English name was given afterwards based on the new circumstances at that time (like the extended edu scope, the new global era or the future influence).
So, again, it is NOT a simple translation, the translation doesn't match because of the history.