I noticed that the Torah never call this day of Yom Teruah with the name Rosh HaShana. So how en when did it got the name Rosh HaShana? And more important how does one relate the terms 'Rosh HaShana' with those of Yom Teruah and Yom HaZikaron?
Rosh hashona literally means "the head/beginning of the year"; it's simply an adjective and not a noun. (The day doesn't need to be given the name "Rosh Hashona" any more than the first born child needs to be given the name "oldest child".)
But if you want a source, see Mishan, Rosh Hashonah, which beging "There are four Rosh Hashana's" and lists this day as one of them