To further the original question, 'שבת זכור' is wordplay on the Pasuk:
זכור את יום השבת לקדשו
Remember the Shabbat day for his holiness.
Thus, it appropriate that only men should come to shul on Shabbat Zachor.
However, the women began to feel left out and forgotten. Thus, they tried to change the name to שבת זכירה, the 'Shabbat of her remembrance'. The Gemara in Megillah 2b states:
אשכחן עשייה זכירה מנלן
We have found the practice of making a (Shabbat) Zechira-- from where is the source?
The Gemara answers based on a Pasuk:
והימים האלה נזכרים ונעשים איתקש זכירה לעשייה
'And these days are Zechira-d and practiced'-- it connects Zechira to actual practice.
This is a stamp of approval on the practice of שבת זכירה. However, the Gemara continues:
דלא כי האי תנא דתניא רבי יהושע בן קרחה אומר כרכין המוקפין חומה מימות אחשורוש קורין
(This ruling) is not like this tanna (R' Yehoshua ben Levi), as Rabbi Yehoshua ben Levi, taught: (Only) cities walled from the time of Achashverosh read (the verse in this manner).
Now, the Sanhedrin was centered in Teveria, about which we learn in a different discussion (ibid. 5b):
חזקיה קרי בטבריא בארביסר ובחמיסר מספקא ליה אי מוקפת חומה מימות
Chizkiyah read (the Megillah) in Teveria on the fourteenth and the fifteenth, from the doubt over whether it was walled from the time (of Achashveirosh; reading megillah on the 15th and reading the Pasuk as sanctioning שבת זכירה are a package deal for walled cities).
Thus, the Teveria-based Sanhedrin were unsure which way they were supposed to read the Pasuk. As such, we ended up with a compromise: Women can come to shul on this Shabbat, but it would be called by its original name, שבת זכור.