Authenticator is a genuine App from the App Store, that I think is rather redundant now that phone OSs have evolved. It’s basically a repository of passwords.
We downloaded it a long while back when the company I was with used it for collating some company security stuff, but then we never used it once it was highlighted that while it’s compliant with basic app guidelines, it probably also stores your data elsewhere, not so compliantly.
So, delete it.

Here’s another thing. A lot of locals let the phone shop set up their phones for them, and they quite often end up with a clone of a clone of a clone… The other half is bad at that. Someone may well have downloaded the app based on ‘helpful’ advice.

Be selective about who you lend the phone to. If you must, track down all your spares, set up a separate Apple ID for ‘family’ to keep your stuff separate from theirs, and all your spares. And change all your current passwords.


Edit. On second looking, The one in the OP is similar to the one that the company used, which was microShiite related. But basically the same thing. Password and login storage. Still probably redundant. I’d still take some extra care with who uses the phone in your absence.