Something’s fishy here. Shira is a Zionistic name??? Is Shabbos Shira a Zionistic holiday. Isn’t there a medrash that there were 9 Shiros so far, and the tenth will be in the time of moshiach.
Totally agree with the kashya from Alexander, and I think there is even an Amora or Tanna with that name.
What about Chiya, Papa, Rafram, Ayvu, Antignos, Horknos? All were Tannaim and Amoraim. Many others similar. The Shulchan Oruch even has a whole siman dedicated to how to spell names for a get. It lists names like Roza, Raizel, Feiga, etc.