Leviticus 23:15 says (JPS):
וּסְפַרְתֶּ֤ם לָכֶם֙ מִמָּחֳרַ֣ת הַשַּׁבָּ֔ת מִיּוֹם֙ הֲבִ֣יאֲכֶ֔ם אֶת־עֹ֖מֶר הַתְּנוּפָ֑ה שֶׁ֥בַע שַׁבָּת֖וֹת תְּמִימֹ֥ת תִּהְיֶֽינָה׃
And ye shall count unto you from the morrow after the day of rest, from the day that ye brought the sheaf of the waving; seven weeks shall there be complete;
The term ספירת העומר means "counting of the omer". We're not counting the sheaves themselves. We're counting the days that follow the bringing of an offering on the 2nd day of Pesach. Perhaps, a better term would be ספירת הימים אחר העומר - "Counting of the days after the Omer", or something similar.
Even the actual counting itself, we say, "Z days (weeks) to (or "of") the Omer". This seems confusing or misleading, as it seems to indicate that the omer was brought every day for 50 (49) days!
Is there some other meaning within the usage of this term, perhaps?
Note - The number 50 in the title is left there, intentionally: See here.