To ensure its grip on the message put out by its domestic and international broading service,including CGTN,the government consolidated them in March into a single media group as known Voice of China (its name in English perhaps consciously echoing that of the American govrenment`s broading service,Voice of America).

括号its name````里的内容，似乎没有谓语 所以不是一个完整的句子对吗？

that of ，that 又是指代什么呢?

括号内不是一个句子，而是独立主格结构作状语，对主句作补充说明。如果去掉括号，则用逗号和主句隔开。其中echoing为现在分词，its name in English为现在分词的逻辑主语。that为名词替代词，替代前面出现过的一个特指的单数名词或不可数名词，在这里that替代the name.

另外，网友句子中的 as known为笔误，应为 known as.