can I get this women fired for this?

[James K]

If she is naming names, and particularly naming the bank and names, then you could ask to see an officer of the bank to render your complaint. Bring printed screen shots of the Facebook page as evidence.

That said, folk talk about their jobs all the time. As long as she is not giving out personal information or any way to identify the people she is speaking of, try reversing the situation for your own job. Have you never spoken about folk that you work with or customers in a way that someone might "take offence" and look to have your head (or job) on a pike?