Yes, but trinary honestly makes more sense in contemporary English. I'm not sure whether preserving Greco-Latin roots or selecting for usability is more important here.
Update: there's also the "Ternary tree", the "Ternary search tree", the "Ternary heap", and the "Ternary numeral system". Most have even Wikipedia articles. There is no Wikipedia article for anything "Trinary" related to computer science.