Where did the word “trinity” originate?
The following excerpt from Basic Thelogy by Charles Ryrie should answer your question.
The early church fathers did not formulate any clear statement concerning the Trinity. Some were unclear about the Logos, and most were unconcerned about giving attention to the Spirit except for His work in the lives of believers. In answer to Praxeus, Tertullian (ca. 165-220) asserted the threeness aspect of God, being the first to use the word Trinity. However, he did not have a full and accurate understanding of the Trinity, his views being tinged with subordinationism.