Related to this question (about the reason for the name), what is the source or origin of calling the Shabbat on which we read Shirat Hayam Shabbat Shira?
We don't call the week on which we read the Shirat Hab'er a Shabbat Shira though its content is no less a Shir and the events of Matan Torah are no less unifying or miraculous but we have nothing called "Shabbat Matan Torah" or an equivalent.
What was the process by which this particular Shabbat became known by a specific name whereas others were not labelled?