Tefilas Mincha----- Mincha? What does that Mean?

  

Tosafos in Pesachim 107A says that Tefilas "Mincha" is called "Mincha" because Minchas Chavitin was brought at that time. There were two Minchas Chavitin, one in the morning and one after Chatzos Hayom, however since Eliyahu Hanovi was answered when he prayed at that time which is an "Eis Ratzon" which also happened to be the time of the Minchas Chavitin that is why we call it Tefilas Mincha. I find that pshat on its surface very forced. Maybe Tosafos means something deeper that I haven't understood. The vilna shas has printed next to that Tosafos an Abudraham that says that it comes from the Targum on the pasuk וַיִּשְׁמְע֞וּ אֶת־ק֨וֹל יְהֹוָ֧ה אֱלֹהִ֛ים מִתְהַלֵּ֥ךְ בַּגָּ֖ן לְר֣וּחַ הַיּ֑וֹם

The Targum says לְר֣וּחַ הַיּ֑וֹם "Lemanach Yoma" and that was the tenth hour which is Mincha time and that is how it got its name. What does that mean? what does the word "Manach" mean? what the relationship? I don't have answers to this pshat. I was thinking something much simpler. The Chinuch in Mitzva 116 discusses why a Korban Mincha is called "Mincha" and he says

הדומה לפי הפשט, כי על כן יקרא מנחה מפני שענינה מעט מקרבן בעל חיים כמו             שמנחות בני אדם יהיו במועט ברב הפעמים                                                  

Simply, the Mincha is the smallest one.