We know that the word תפילין appears nowhere in the Tanach. On the other hand, the only meaning of "תפילה" in Tanach is "a prayer" (see Sefaria search תפילה").
Seemingly, because the commandment of Teffilin is Biblical, it has no connection with the Rabbinic obligation of fixed prayers, to necessitate the word תפילין (single תפילה").
The "Dictionary of Jewish Usage: A Guide to the Use of Jewish Terms" (quoted on WIKI) says:
I thought I could give it a try here, to find a better explanation of the origin of the word "תפילין".