I've only seen
Ira in use once in non-biblical Jewish history (In R.
Natan Sternherz's "Names of the Righteous", where he lists off the names of righteous men and women from jewish history up to the 1800s, with more names being added in later editions. Here,
Ira is a name of a rabbi from Wallachia). It seems
Ira really kicked off when droves of East-European Jews migrated to the US, in the early 1900s, and started using
Ira and
Irving as Americanised forms of
Israel and other jewish names. Obviously that didn't work in the assimilation route, as those names are now almost exclusively Jewish-american.