【原创】这个怎么翻译好？

I think you are right.

参考国外各种大学名称的写法，我觉得可以写成
Zhejiang ,Fujian and Taiwan Club of Economy and Culture，
或者Zhejiang ,Fujian and Taiwan Club of Economic and Cultural Exchange

熊猫，这样如何？Zhejiang,Fujian and Taiwan Club for Economic and Cultural Exchange

I searched with google using the keywords (“economic and cultural exchange”, club), (“economic and cultural exchange”, center), (“economic and cultural exchange”, association) and found that “economic and cultural exchange” is generally followed by the organization (i.e. economic and cultural exchange club, economic and cultural exchange center, economic and cultural association; but Association for the Economic and Cultural Exchange was also found)

值得参考

ruojun 老师和楼上，一个是of ，一个用 for

两者有什么区别和联系么

我个人觉得of比较好，读起来语感比较好（可能也是这种用法比较多的缘故吧）。of：是什么的意思；for：就有为什么而做的意思（目的性，指向性比较强）。
其实这几句表达都行的（你的有点中国化），具体的就不要太讲究啦。

在网上查到的:
河 南 经 济 文 化 翻 译 中 心
Henan Translation Center For Economic & Cultural Exchange

感觉这个和楼主的句型差不多

Economic and Cultural Exchange Club of Zhejiang ,Fujian and Taiwan