This seems to be a case of putting the object before the verb. This is quite common in Chinese. They do it when the object is in fact the topic of the sentence. In English, when the object wants to be the topic, we make the verb passive and change the object to subject. E.g. test finished. In Chinese there is no need to do this. You just plonk the object before the verb and bob's your uncle!

考试已经结束了。

我考完了means you have finished the exam,完成考试don`t have a subject,it just focus on the verb “finish”,it could be anyone。 like I finish my job and job done .

我考完试了 这句话有主语 意思是“我” 完成了“考试” 完成考试 是一个动宾短语 也就是一个动词+名词，这句话没有主语，也可以是你完成考试，他完成考试。

考試 是 離合詞 請參閱 http://twtcsl.org/further/Separable+Words_lianmianci